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Solve Equations with Variables on Both Sides using the Distributive Property
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Question 1 of 19
1. Question
Solve`6(2m+5)-5(3m+2)=26`- `m=` (-2)
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Distributive Property
`a``(b+c)=``a``b+``a``c`To solve for `m`, it needs to be alone on one side.Start by expanding the left side of the equation by using the Distributive Property.`6``(2``m` `+5)` `-5``(3``m` `+2)` `=` `26` `6``(2``m``)+``6``(5)` `-5``(3``m``)` `-5``(2)` `=` `26` `12``m` `+30-15``m` `-10` `=` `26` `-3``m` `+20` `=` `26` Next, move `20` to the other side by subtracting `20` from both sides of the equation.`-3``m` `+20` `=` `26` `-3``m` `+20` `-20` `=` `26` `-20` `-3``m` `=` `6` `20-20` cancels out Finally, remove `-3` by dividing both sides of the equation by `-3`.`-3``m` `=` `6` `-3``m``divide-3` `=` `6``divide-3` `m` `=` `-2` `-3divide-3` cancels out Check our workTo confirm our answer, substitute `m=-2` to the original equation.`6(2m+5)-5(3m+2)` `=` `26` `6(2(-2)+5)-5(3(-2)+2)` `=` `26` Substitute `m=-2` `6(-4+5)-5(-6+2)` `=` `26` `6(1)-5(-4)` `=` `26` `6+20` `=` `26` `26` `=` `26` Since the equation is true, the answer is correct.`m=-2`Hint
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Question 2 of 19
2. Question
Solve`8(2y+3)-4(3y+2)=32`- `y=` (4)
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When moving a term to the other side of an equation, the operation is inversed.Distributive Property
`a``(b+c)=``a``b+``a``c`To solve for `y`, it needs to be alone on one side.Start by expanding the left side of the equation by using the Distributive Property.`8``(2``y` `+3)-``4``(3``y` `+2)` `=` `32` `8``(2``y``)+``8``(3)` `-4``(3``y``)` `-4``(2)` `=` `32` `16``y` `+24-12``y``-8` `=` `32` `4``y` `+16` `=` `32` Next, move `16` to the other side by subtracting `16` from both sides of the equation.`4``y` `+16` `=` `32` `4``y` `+16` `-16` `=` `32` `-16` `4``y` `=` `16` `16-16` cancels out Finally, remove `4` by dividing both sides of the equation by `4`.`4``y` `=` `16` `4``y``divide4` `=` `16``divide4` `y` `=` `4` `4divide4` cancels out Check our workTo confirm our answer, substitute `y=4` to the original equation.`8(2y+3)-4(3y+2)` `=` `32` `8[2(4)+3]-4[3(4)+2]` `=` `32` Substitute `y=4` `8(8+3)-4(12+2)` `=` `32` `8(11)-4(14)` `=` `32` `88-56` `=` `32` `32` `=` `32` Since the equation is true, the answer is correct.`y=4`Hint
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Question 3 of 19
3. Question
Solve`9(m+1)=3(m-3)`- `m=` (-3)
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Incorrect
Help VideoInverse Operations
When moving a term to the other side of an equation, the operation is inversed.Distributive Property
`a``(b+c)=``a``b+``a``c`To solve for `m`, it needs to be alone on one side.Start by expanding the left side of the equation by using the Distributive Property.`9``(``m` `+1)` `=` `3``(``m` `-3)` `9``(``m``)+``9``(1)` `=` `3``(``m``)+``3``(-3)` `9``m` `+9` `=` `3``m` `-9` Next, move `9` to the other side by subtracting `9` from both sides of the equation.`9``m` `+9` `=` `3``m` `-9` `9``m` `+9` `-9` `=` `3``m` `-9` `-9` `9``m` `=` `3``m` `-18` `9-9` cancels out Now, move `3m` to the other side by subtracting `3m` from both sides of the equation.`9``m` `=` `3``m` `-18` `9``m` `-3m` `=` `3``m` `-18` `-3m` `6``m` `=` `-18` `3m-3m` cancels out Finally, remove `6` by dividing both sides of the equation by `6`.`6``m` `=` `-18` `6``m``divide6` `=` `-18``divide6` `m` `=` `-3` `6divide6` cancels out Check our workTo confirm our answer, substitute `m=-3` to the original equation.`9(m+1)` `=` `3(m-3)` `9(-3+1)` `=` `3(-3-3)` Substitute `m=-3` `9(-2)` `=` `3(-6)` `-18` `=` `-18` Since the equation is true, the answer is correct.`m=-3`Hint
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Question 4 of 19
4. Question
Solve`2a+5=6(a-4)-3a`- `a=` (29)
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Help VideoInverse Operations
When moving a term to the other side of an equation, the operation is inversed.Distributive Property
`a``(b+c)=``a``b+``a``c`To solve for `a`, it needs to be alone on one side.Start by expanding the right side of the equation by using the Distributive Property.`2``a` `+5` `=` `6``(``a` `-4)-3``a` `2``a` `+5` `=` `6``a` `-``6``(4)-3``a` `2``a` `+5` `=` `3``a` `-24` Next, move `2a` to the other side by subtracting `2a` from both sides of the equation.`2``a` `+5` `=` `3``a` `-24` `2``a` `+5` `-2a` `=` `3``a` `-24` `-2a` `5` `=` `a` `-24` `2a-2a` cancels out Now, move `-24` to the other side by adding `24` to both sides of the equation.`5` `=` `a` `-24` `5` `+24` `=` `a` `-24` `+24` `29` `=` `a` `-24+24` cancels out `a` `=` `29` Check our workTo confirm our answer, substitute `a=29` to the original equation.`2a+5` `=` `6(a-4)-3a` `2(29)+5` `=` `6(29-4)-3(29)` Substitute `a=29` `58+5` `=` `6(25)-87` `63` `=` `150-87` `63` `=` `63` Since the equation is true, the answer is correct.`a=29`Hint
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Question 5 of 19
5. Question
Solve`7(m+2)+2(6-2m)=4m`- `m=` (26)
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Help VideoInverse Operations
When moving a term to the other side of an equation, the operation is inversed.Distributive Property
`a``(b+c)=``a``b+``a``c`To solve for `m`, it needs to be alone on one side.Start by expanding the left side of the equation by using the Distributive Property.`7``(``m` `+2)+``2``(6-2``m``)` `=` `4``m` `7``m` `+``7``(2)+``2``(6)+``2``(-2``m``)` `=` `4``m` `7``m` `+14+12-4``m` `=` `4``m` `3``m` `+26` `=` `4``m` Next, move `3m` to the other side by subtracting `3m` from both sides of the equation.`3``m` `+26` `=` `4``m` `3``m` `+26` `-3m` `=` `4``m` `-3m` `26` `=` `m` `3m-3m` cancels out `m` `=` `26` Check our workTo confirm our answer, substitute `m=26` to the original equation.`7(m+2)+2(6-2m)` `=` `4m` `7(26+2)+2(6-2(26))` `=` `4(26)` Substitute `m=26` `7(28)+2(6-52)` `=` `104` `196+2(-46)` `=` `104` `196-92` `=` `104` `104` `=` `104` Since the equation is true, the answer is correct.`m=26`Hint
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Question 6 of 19
6. Question
Solve`2(y+3)+5(y+2)=4(9-4y)-3(16-3y)`- `y=` (-2)
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Help VideoInverse Operations
When moving a term to the other side of an equation, the operation is inversed.Distributive Property
`a``(b+c)=``a``b+``a``c`Get `y` alone to the left side and all constants to the right.Start by expanding both sides of the equation by using the Distributive Property.`2``(``y` `+3)+` `5``(``y` `+2)` `=` `4``(9-4``y``)-` `3``(16-3``y``)` `2``y``+` `2``(3)+` `5``y``+` `5``(2)` `=` `4``(9)-` `4``(4``y``)-` `3``(16)-` `3``(-3``y``)` `2``y` `+6+5``y``+10` `=` `36-16``y` `-48+9``y` `7``y` `+16` `=` `-7``y` `-12` Next, move `16` to the other side by subtracting `16` from both sides of the equation.`7``y` `+16` `=` `-7``y` `-12` `7``y` `+16` `-16` `=` `-7``y` `-12` `-16` `7``y` `=` `-7``y` `-28` `16-16` cancels out Then, move `-7y` to the other side by adding `7y` to both sides of the equation.`7``y` `=` `-7``y` `-28` `7``y` `+7y` `=` `-7``y` `-28` `+7y` `14``y` `=` `-28` `-7y+7y` cancels out Finally, remove `14` by dividing both sides of the equation by `14`.`14``y` `=` `-28` `14``y``-:14` `=` `-28``-:14` `y` `=` `-2` `14divide14` cancels out Check our workTo confirm our answer, substitute `y=-2` to the original equation.`2(y+3)+5(y+2)` `=` `4(9-4y)-3(16-3y)` `2(-2+3)+5(-2+2)` `=` `4(9-4(-2))-3(16-3(-2))` Substitute `y=-2` `2(1)+5(0)` `=` `4(9+8)-3(16+6)` `2+0` `=` `4(17)-3(22)` `2` `=` `68-66` `2` `=` `2` Since the equation is true, the answer is correct.`y=-2`Hint
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Question 7 of 19
7. Question
Solve for `a``3(2a-4)=4a-6`- `a=` (3)
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Help VideoTo solve for `a`, get `a` by itselfDistribute the value inside the parenthesis.`3``(2a-4)` `=` `4a-6` `(2axx``3``)-(4xx``3``)` `=` `4a-6` `6a-12` `=` `4a-6` Get the `a` variable on one side of the equation`6a-12` `-4a` `=` `4a-6` `-4a` Subtract `4a` from both sides `6a-12` `-4a` `=` `4a``-6` `-4a` `4a-4a` cancels out `2a-12` `=` `-6` `2a-12` `+12` `=` `-6` `+12` Add `12` to both sides `2a``-12` `+12` `=` `-6` `+12` `-12+12` cancels out `2a` `=` `6` `2a``divide2` `=` `6``divide2` Divide both sides by `2` `2``a``divide2` `=` `6``divide2` `times2divide2` cancels out `a` `=` `3` `a=3`Hint
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Question 8 of 19
8. Question
Solve for `x``5(2x+7)-6x=8+x`- `x=` (-9)
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Help VideoTo solve for `x`, get `x` by itselfDistribute the value inside the parenthesis.`5``(2x+7)-6x` `=` `8+x` `(2x xx``5``)+(7xx``5``)-6x` `=` `8+x` `10x+35-6x` `=` `8+x` `4x+35` `=` `8+x` Get the `x` variable on one side of the equation`4x+35` `-x` `=` `8+x` `-x` Subtract `x` from both sides `4x+35` `-x` `=` `8``+x` `-x` `x-x` cancels out `3x+35` `=` `8` `3x+35` `-35` `=` `8` `-35` Subtract `35` from both sides `3x``+35` `-35` `=` `8` `-35` `35-35` cancels out `3x` `=` `-27` `3x``divide3` `=` `-27``divide3` Divide both sides by `3` `3``x``divide3` `=` `-27``divide3` `times3divide3` cancels out `x` `=` `-9` `x=-9`Hint
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Question 9 of 19
9. Question
Solve for `x``6(x+2)-4(x-1)=20`- `x=` (2)
Correct
Correct!
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Help VideoTo solve for `x`, get `x` by itselfDistribute the value inside the parenthesis.`6``(x+2)``-4``(x-1)` `=` `20` ` ` ` ` ` ` `6``(x+2)` `=` `(x xx``6``)+(2xx``6``)` ` ` `=` `6x+12` ` ` ` ` ` ` `-4``(x-1)` `=` `(x xx``(-4)``)+(-1xx``(-4)``)` ` ` `=` `-4x+4` ` ` ` ` ` ` `(6x+12)``+``(-4x+4)` `=` `20` `2x+16` `=` `20` Subtract `16` from both sides of the equation`2x+16` `-16` `=` `20` `-16` `2x``+16` `-16` `=` `20` `-16` `16-16` cancels out `2x` `=` `4` `2x``divide2` `=` `4``divide2` Divide both sides by `2` `2``x``divide2` `=` `4``divide2` `times2divide2` cancels out `x` `=` `2` `x=2`Hint
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Question 10 of 19
10. Question
Solve for `v``-8v+7(v+8)=32-7v`- `v=` (-4)
Correct
Well Done
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To solve for `v`, get `v` by itselfDistribute the value inside the parenthesis.`-8v``+7``(v+8)` `=` `32-7v` `-8v+((v xx``7``)+(8xx``7``))` `=` `32-7v` `-8v+7v+56` `=` `32-7v` `-v+56` `=` `32-7v` Get the `v` variable on one side of the equation`-v+56` `+7v` `=` `32-7v` `+7v` Add `7v` to both sides `-v+56` `+7v` `=` `32``-7v` `+7v` `-7v+7v` cancels out `6v+56` `=` `32` `6v+56` `-56` `=` `32` `-56` Subtract `56` from both sides `6v``+56` `-56` `=` `32` `-56` `56-56` cancels out `6v` `=` `-24` `6v``-:6` `=` `-24``-:6` Divide both sides by `6` `6``v``-:6` `=` `-24``-:6` `times6divide6` cancels out `v` `=` `-4` `v=-4` -
Question 11 of 19
11. Question
Solve for `k``11-5k=4+7(1-5k)`- `k=` (0)
Correct
Well Done!
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To solve for `k`, get `k` by itselfDistribute the value inside the parenthesis.`11-5k` `=` `4``+7``(1-5k)` `11-5k` `=` `4+((1 xx``7``)+(-5k xx``7``))` `11-5k` `=` `4+7-35k` `11-5k` `=` `11-35k` Get the `k` variable on one side of the equation`11-5k` `+5k` `=` `11-35k` `+5k` Add `5k` to both sides `11``-5k` `+5k` `=` `11-35k` `+5k` `-5k+5k` cancels out `11` `=` `11-30k` `11` `-11` `=` `11-30k` `-11` Subtract `11` from both sides `11` `-11` `=` `11``-30k` `-11` `11-11` cancels out on both sides `0` `=` `-30k` `0``-:(-30)` `=` `30k``-:(-30)` Divide both sides by `-30` `0``-:(-30)` `=` `30``k``-:(-30)` `times(-30)divide(-30)` cancels out `0` `=` `k` `k` `=` `0` `k=0` -
Question 12 of 19
12. Question
Solve for `n``3(n+8)=3(2n-2)`- `n=` (10)
Correct
Excellent!
Incorrect
To solve for `n`, get `n` by itselfDistribute the value inside the parenthesis.`3``(n+8)` `=` `3``(2n-2)` `(n xx``3``)+(8xx``3``)` `=` `(2n xx``3``)+(-2xx``3``)` `3n+24` `=` `6n-6` Get the `n` variable on one side of the equation`3n+24` `-24` `=` `6n-6` `-24` Subtract `24` from both sides `3n``+24` `-24` `=` `6n-6` `-24` `24-24` cancels out `3n` `=` `6n-30` `3n` `-6n` `=` `6n-30` `-6n` Subtract `6n` from both sides `3n` `-6n` `=` `6n``-30` `-6n` `6n-6n` cancels out `-3n` `=` `-30` `-3n``divide(-3)` `=` `-30``divide(-3)` Divide both sides by `-3` `-3``n``divide(-3)` `=` `-30``divide(-3)` `times(-3)divide(-3)` cancels out `n` `=` `10` `n=10` -
Question 13 of 19
13. Question
Solve`-4(2y-3)=1/2(12-4y)`- `y=` (1)
Correct
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Help VideoInverse Operations
When moving a term to the other side of an equation, the operation is inversed.Distributive Property
`a``(b+c)=``a``b+``a``c`To solve for `y`, it needs to be alone on one side.Start by expanding the left side of the equation by using the Distributive Property.`-4``(2``y` `-3)` `=` `1/2``(12-4``y``)` `-4``(2``y``)` `-4``(-3)` `=` `1/2``(12)+``1/2``(-4``y``)` `-8``y` `+12` `=` `6-2``y` Next, move `-2y` to the other side by adding `2y` to both sides of the equation.`-8``y` `+12` `=` `6-2``y` `-8``y` `+12` `+2y` `=` `6-2``y` `+2y` `-6``y` `+12` `=` `6` `-2y+2y` cancels out Now, move `12` to the other side by subtracting `12` from both sides of the equation.`-6``y` `+12` `=` `6` `-6``y` `+12` `-12` `=` `6` `-12` `-6``y` `=` `-6` `12-12` cancels out Finally, remove `-6` by dividing both sides of the equation by `-6`.`-6``y` `=` `-6` `-6``y``divide-6` `=` `-6``divide-6` `y` `=` `1` `6divide6` cancels out Check our workTo confirm our answer, substitute `y=1` to the original equation.`-4(2y-3)` `=` `1/2(12-4y)` `-4[2(1)-3]` `=` `1/2[12-4(1)]` Substitute `y=1` `-4(2-3)` `=` `1/2(12-4)` `-4(-1)` `=` `1/2(8)` `4` `=` `4` Since the equation is true, the answer is correct.`y=1`Hint
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Question 14 of 19
14. Question
Solve`2/3(n-5)=3/4(2n+10)`- `n=` (-13)
Correct
Correct!
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Help VideoInverse Operations
When moving a term to the other side of an equation, the operation is inversed.Distributive Property
`a``(b+c)=``a``b+``a``c`Get `n` alone to the left side and all constants to the right.First, remove the fractions by finding the Least Common Denominator `(LCD)` of the denominators `4` and `3`.Multiples of `3`:`3 6 9` `12` `15`Multiples of `4`:`4 8` `12` `16 20`The `LCD` of `3` and `4` is `12`Multiply the `LCD` to both sides of the equation to remove the fractions. Use the Distributive Property.$$\frac{2}{3}(\color{#00880A}{n}-5)\color{#D800AD}{\times12}$$ `=` $$\frac{3}{4}(2\color{#00880A}{n}+10)\color{#D800AD}{\times12}$$ $$\frac{24}{3}(\color{#00880A}{n}-5)$$ `=` $$\frac{36}{4}(2\color{#00880A}{n}+10)$$ `8``(``n` `-5)` `=` `9``(2``n` `+10)` `8``n` `+``8``(-5)` `=` `9``(2``n``)+``9``(10)` `8``n` `-40` `=` `18``n` `+90` Simplify Next, move `8n` to the other side by subtracting `8n` from both sides of the equation.`8``n` `-40` `=` `18``n` `+90` `8``n` `-40` `-8n` `=` `18``n` `+90` `-8n` `-40` `=` `10``n` `+90` `8n-8n` cancels out Now, move `90` to the other side by subtracting `90` from both sides of the equation.`-40` `=` `10``n` `+90` `-40` `-90` `=` `10``n` `+90` `-90` `-130` `=` `10``n` `90-90` cancels out Finally, remove `10` by dividing both sides of the equation by `10`.`-130` `=` `10``n` `-130``divide10` `=` `10``n``divide10` `-13` `=` `n` `10divide10` cancels out `n` `=` `-13` Check our workTo confirm our answer, substitute `n=-13` to the original equation.`2/3(n-5)` `=` `3/4(2n+10)` `2/3(-13-5)` `=` `3/4(2(-13)+10)` Substitute `n=-13` `2/3(-18)` `=` `3/4(-26+10)` `(-36)/3` `=` `3/4(-16)` `-12` `=` `(-48)/4` `-12` `=` `-12` Since the equation is true, the answer is correct.`n=-13`Hint
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Question 15 of 19
15. Question
Solve for `x``(x+8)/3 = x`- `x=` (4)
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Help VideoTo solve for `x`, get `x` by itselfMultiply both sides of the equation by `3``frac{x+8}{3}``times3` `=` `x``times3` `frac{3(x+8)}{3}` `=` `x``times3` `x+8` `=` `3x` The coefficient `frac{3}{3}` cancels out Now subtract `x` from both sides of the equation`x+8` `-x` `=` `3x` `-x` `x``+8` `-x` `=` `3x` `-x` `x-x` cancels out `8` `=` `2x` Finally, divide both sides of the equation by `2``8``divide2` `=` `2x``divide2` `8``divide2` `=` `2``x``divide2` `times2divide2` cancels out `4` `=` `x` `x` `=` `4` `x=4`Hint
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Question 16 of 19
16. Question
Solve`(3(p-3))/4=(2(2p-7))/5`- `p=` (11)
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Help VideoInverse Operations
When moving a term to the other side of an equation, the operation is inversed.Distributive Property
`a``(b+c)=``a``b+``a``c`Get `p` alone to the left side and all constants to the right.First, remove the fractions by finding the Least Common Denominator `(LCD)` of the denominators `4` and `5`.Multiples of `4`:`4 8 12 16` `20`Multiples of `5`:`5 10 15` `20` `25`The `LCD` of `4` and `5` is `20`Multiply the `LCD` to both sides of the equation to remove the fractions. Use the Distributive Property.$$\left[\frac{3(\color{#00880A}{p}-3)}{4}\right]\color{#D800AD}{\times20}$$ `=` $$\left[\frac{2(2\color{#00880A}{p}-7)}{5}\right]\color{#D800AD}{\times20}$$ $$\frac{20\times3}{4}(\color{#00880A}{p}-3)$$ `=` $$\frac{20\times2}{5}(2\color{#00880A}{p}-7)$$ $$\frac{60}{4}(\color{#00880A}{p}-3)$$ `=` $$\frac{40}{5}(2\color{#00880A}{p}-7)$$ `15``(``p` `-3)` `=` `8``(2``p` `-7)` `15``p` `+``15``(-3)` `=` `8``(2``p``)+``8``(-7)` `15``p` `-45` `=` `16``p` `-56` Simplify Next, move `15p` to the other side by subtracting `15p` from both sides of the equation.`15``p` `-45` `=` `16``p` `-56` `15``p` `-45` `-15p` `=` `16``p` `-56` `-15p` `-45` `=` `p` `-56` `15p-15p` cancels out Finally, move `-56` to the other side by adding `56` to both sides of the equation.`-45` `=` `p` `-56` `-45` `+56` `=` `p` `-56` `+56` `11` `=` `p` `-56+56` cancels out `p` `=` `11` Check our workTo confirm our answer, substitute `p=11` to the original equation.`(3(p-3))/4` `=` `(2(2p-7))/5` `(3(11-3))/4` `=` `(2(2(11)-7))/5` Substitute `p=11` `(3(8))/4` `=` `(2(22-7))/5` `24/4` `=` `(2(15))/5` `24/4` `=` `30/5` `6` `=` `6` Since the equation is true, the answer is correct.`p=11`Hint
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Question 17 of 19
17. Question
Solve for `x``(2x+5)/4 = (x-1)/3`- `x=` (-19/2)
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Help VideoTo solve for `x`, get `x` by itselfMultiply both sides of the equation by `4``frac{2x+5}{4}``times4` `=` `frac{x-1}{3}``times4` `frac{4(2x+5)}{4}` `=` `frac{x-1}{3}``times4` `2x+5` `=` `frac{4(x-1)}{3}` The coefficient `frac{4}{4}` cancels out `2x+5` `=` `frac{(x xx 4)-(1xx4)}{3}` Distribute the value inside the parenthesis `2x+5` `=` `frac{4x-4}{3}` Next, multiply both sides of the equation by `3``(2x+5)``times3` `=` `frac{4x-4}{3}``times3` `(2x+5)``times3` `=` `frac{3(4x-4)}{3}` `3(2x+5)` `=` `4x-4` The coefficient `frac{3}{3}` cancels out `(2x xx 3)+(5xx3)` `=` `4x-4` Distribute the value inside the parenthesis `6x+15` `=` `4x-4` Now, subtract `4x` from both sides of the equation`6x+15` `-4x` `=` `4x-4` `-4x` `6x+15` `-4x` `=` `4x``-4` `-4x` `4x-4x` cancels out `2x+15` `=` `-4` Now, subtract `15` from both sides of the equation`2x+15` `-15` `=` `-4` `-15` `2x``+15` `-15` `=` `-4` `-15` `15-15` cancels out `2x` `=` `-19` Finally, divide both sides of the equation by `2`.`2x``divide2` `=` `-19``divide2` `2``x``divide2` `=` `-19``divide2` `times2divide2` cancels out `x` `=` `-frac{19}{2}` `x=-frac{19}{2}`Hint
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Question 18 of 19
18. Question
Solve for `x``(3x+1)/5 = (2x-1)/2`- `x=` (7/4)
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Help VideoTo solve for `x`, get `x` by itselfMultiply both sides of the equation by `5``frac{3x+1}{5}``times5` `=` `frac{2x-1}{2}``times5` `frac{5(3x+1)}{5}` `=` `frac{2x-1}{2}``times5` `3x+1` `=` `frac{5(2x-1)}{2}` The coefficient `frac{5}{5}` cancels out `3x+1` `=` `frac{(2x xx 5)-(1xx5)}{3}` Distribute the value inside the parenthesis `3x+1` `=` `frac{2x-5}{3}` Next, multiply both sides of the equation by `2``(3x+1)``times2` `=` `frac{10x-5}{2}``times2` `(3x+1)``times2` `=` `frac{2(10x-5)}{2}` `2(3x+1)` `=` `10x-5` The coefficient `frac{2}{2}` cancels out `(3x xx 2)+(1xx2)` `=` `10x-5` Distribute the value inside the parenthesis `6x+2` `=` `10x-5` Now, subtract `10x` from both sides of the equation`6x+2` `-10x` `=` `10x-5` `-10x` `6x+2` `-10x` `=` `10x``-5` `-10x` `10x-10x` cancels out `-4x+2` `=` `-5` Now, subtract `2` from both sides of the equation`-4x+2` `-2` `=` `-5` `-2` `-4x``+2` `-2` `=` `-5` `-2` `2-2` cancels out `-4x` `=` `-7` Finally, divide both sides of the equation by `-4`.`-4x``divide(-4)` `=` `-7``divide(-4)` `=` `-7``divide(-4)` `times(-4)divide(-4)` cancels out `x` `=` `7/4` `x=frac{7}{4}`Hint
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Question 19 of 19
19. Question
Solve for `x``(x+3)/6-(x-1)/5=1/3`- `x=` (11)
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Exceptional!
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Help VideoTo solve for `x`, get `x` by itself`6`, `5` and `3` has `30` as a common denominatorMake sure that fractions have the common denominator which is `30``frac{x+3}{6}-frac{x-1}{5}` `=` `1/3` `frac{x+3}{6}``timesfrac{5}{5}``-frac{x-1}{5}``timesfrac{6}{6}` `=` `1/3``timesfrac{10}{10}` `frac{5(x+3)}{30}-frac{6(x-1)}{30}` `=` `10/30` Distribute the values inside the parenthesis`(5(x+3))/30-(6(x-1))/30` `=` `10/30` ` ` ` ` ` ` `(5(x+3))/30` `=` `((x xx5)+(3xx5))/30` ` ` `=` `(5x+15)/30` ` ` ` ` ` ` `(6(x-1))/30` `=` `((x xx 6)-(1xx6))/30` ` ` `=` `(6x-6)/30` ` ` ` ` ` ` `(5x+15)/30``-``(6x-6)/30` `=` `10/30` Combine the fractions and find the value of `x``frac{(5x+15)-(6x-6)}{30}` `=` `10/30` `frac{-x+21}{30}` `=` `10/30` Combine like terms `frac{-x+21}{30}``times30` `=` `10/30``times30` Multiply both sides by `30` `frac{30(-x+21)}{30}` `=` `(30(10))/30` `-x+21` `=` `10` The coefficient `frac{30}{30}` cancels out on both sides `-x+21` `-21` `=` `10` `-21` Subtract `21` from both sides `-x``+21` `-21` `=` `10` `-21` `21-21` cancels out `-x` `=` `-11` `(-x)/-1` `=` `(-11)/-1` Divide both sides by `-1` `x` `=` `11` `x=11`Hint
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