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Solve Equations using the Distributive Property
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Question 1 of 11
1. Question
Solve`2(x+4)=12`- `x=` (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 `x`, it needs to be alone on one side.Start by expanding the left side of the equation by using the Distributive Property.`2``(``x` `+4)` `=` `12` `2``x``+``2``(4)` `=` `12` `2``x` `+8` `=` `12` Next, move `8` to the other side by subtracting `8` from both sides of the equation.`2``x` `+8` `=` `12` `2``x` `+8` `-8` `=` `12` `-8` `2``x` `=` `4` `8-8` cancels out Finally, remove `2` by dividing both sides of the equation by `2`.`2``x` `=` `4` `2``x``divide2` `=` `4``divide2` `x` `=` `2` `2divide2` cancels out Check our workTo confirm our answer, substitute `x=2` to the original equation.`2(x+4)` `=` `12` `2[(2)+4]` `=` `12` Substitute `x=2` `2(6)` `=` `12` `12` `=` `12` Since the equation is true, the answer is correct.`x=2`Hint
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Question 2 of 11
2. Question
Solve`8(y-6)=16`- `y=` (8)
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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.`8``(``y` `-6)` `=` `16` `8``y``-``8``(6)` `=` `16` `8``y` `-48` `=` `16` Next, move `48` to the other side by adding `48` to both sides of the equation.`8``y` `-48` `=` `16` `8``y` `-48` `+48` `=` `16` `+48` `8``y` `=` `64` `-48+48` cancels out Finally, remove `8` by dividing both sides of the equation by `8`.`8``y` `=` `64` `8``y``divide8` `=` `64``divide8` `y` `=` `8` `8divide8` cancels out Check our workTo confirm our answer, substitute `y=8` to the original equation.`8(y-6)` `=` `16` `8[(8)-6]` `=` `16` Substitute `y=8` `8(2)` `=` `16` `16` `=` `16` Since the equation is true, the answer is correct.`y=8`Hint
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Question 3 of 11
3. Question
Solve`21=3(t-3)`- `t=` (10)
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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 `t`, it needs to be alone on one side.Start by expanding the right side of the equation by using the Distributive Property.`21` `=` `3``(``t` `-3)` `21` `=` `3``t` `+``3``(-3)` `21` `=` `3``t` `-9` Next, move `-9` to the other side by adding `9` to both sides of the equation.`21` `=` `3``t` `-9` `21` `+9` `=` `3``t` `-9` `+9` `30` `=` `3``t` `-9+9` cancels out Finally, remove `3` by dividing both sides of the equation by `3`.`30` `=` `3``t` `30``divide3` `=` `3``t``divide3` `10` `=` `t` `3divide3` cancels out `t` `=` `10` Check our workTo confirm our answer, substitute `t=10` to the original equation.`21` `=` `3(t-3)` `21` `=` `3(10-3)` Substitute `t=10` `21` `=` `3(7)` `21` `=` `21` Since the equation is true, the answer is correct.`t=10`Hint
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Question 4 of 11
4. Question
Solve`3(14-a)=3`- `a=` (13)
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Well Done!
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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 left side of the equation by using the Distributive Property.`3``(14-``a``)` `=` `3` `3``(14)-``3``a` `=` `3` `42-3``a` `=` `3` Next, move `42` to the other side by subtracting `42` from both sides of the equation.`42-3``a` `=` `3` `42-3``a` `-42` `=` `3` `-42` `-3``a` `=` `-39` `42-42` cancels out Finally, remove `-3` by dividing both sides of the equation by `-3`.`-3``a` `=` `-39` `-3``a``divide-3` `=` `-39``divide-3` `a` `=` `13` `-3divide-3` cancels out Check our workTo confirm our answer, substitute `a=13` to the original equation.`3(14-a)` `=` `3` `3[14-(13)]` `=` `3` Substitute `a=13` `3(1)` `=` `3` `3` `=` `3` Since the equation is true, the answer is correct.`a=13`Hint
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Question 5 of 11
5. Question
Solve`-7(3-y)=-28`- `y=` (-1)
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Great Work!
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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.`-7``(3-``y``)` `=` `-28` `-7``(3)-(``-7``)(``y``)` `=` `-28` `-21+7``y` `=` `-28` Next, move `-21` to the other side by adding `21` to both sides of the equation.`-21+7``y` `=` `-28` `-21+7``y` `+21` `=` `-28` `+21` `7``y` `=` `-7` `-21+21` cancels out Finally, remove `7` by dividing both sides of the equation by `7`.`7``y` `=` `-7` `7``y``divide7` `=` `-7``divide7` `y` `=` `-1` `7divide7` cancels out Check our workTo confirm our answer, substitute `y=-1` to the original equation.`-7(3-y)` `=` `-28` `-7[3-(-1)]` `=` `-28` Substitute `y=-1` `-7(3+1)` `=` `-28` `-7(4)` `=` `-28` `-28` `=` `-28` Since the equation is true, the answer is correct.`y=-1`Hint
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Question 6 of 11
6. Question
Solve for `x``2(x+1)=8`- `x=` (3)
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Great Work!
Incorrect
Help VideoTo solve for `x`, get `x` by itselfDivide both sides of the equation by `2``2(x+1)``divide2` `=` `8``divide2` `2``(x+1)``divide2` `=` `8``divide2` `times2divide2` cancels out `x+1` `=` `4` Finally, subtract `1` from both sides of the equation`x+1` `-1` `=` `4` `-1` `x``+1` `-1` `=` `4` `-1` `1-1` cancels out `x` `=` `3` `x=3`Hint
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Question 7 of 11
7. Question
Solve for `x``5-(3-2x)=10`- `x=` (4)
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Correct!
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Help VideoTo solve for `x`, get `x` by itselfSubtract `5` from both sides of the equation`5-(3-2x)` `-5` `=` `10` `-5` `5``-(3-2x)``-5` `=` `10` `-5` `5-5` cancels out `-3+2x` `=` `5` Distribute negative sign Next, add `3` to both sides of the equation`-3+2x` `+3` `=` `5` `+3` `-3``+2x` `+3` `=` `5` `+3` `-3+3` cancels out `2x` `=` `8` Finally, divide both sides of the equation by `2``2x``divide2` `=` `8``divide2` `2``x``divide2` `=` `8``divide2` `times2divide2` cancels out `x` `=` `4` `x=4`Hint
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Question 8 of 11
8. Question
Solve for `x``2(3-x)=8`- `x=` (-1)
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Keep Going!
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Help VideoTo solve for `x`, get `x` by itselfDivide both sides of the equation by `2``2(3-x)``divide2` `=` `8``divide2` `2``(3-x)``divide2` `=` `8``divide2` `times2divide2` cancels out `3-x` `=` `4` Next, subtract `3` from both sides of the equation`3-x` `-3` `=` `4` `-3` `3` `-x` `-3` `=` `4` `-3` `3-3` cancels out `-x` `=` `1` Finally, make `x` positive by dividing both sides by `-1``-x``divide(-1)` `=` `1``divide(-1)` `x` `=` `-1` `x=-1`Hint
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Question 9 of 11
9. Question
Solve for `k``-9(-8+k)=252`- `k=` (-20)
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Fantastic!
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To solve for `k`, get `k` by itselfDistribute the value inside the parenthesis.`-9``(-8+k)` `=` `252` `((-8)xx``(-9)``)+(kxx``(-9)``)` `=` `252` `72-9k` `=` `252` Get the `k` variable on one side of the equation`72-9k` `-72` `=` `252` `-72` Subtract `72` from both sides `72``-9k` `-72` `=` `252` `-72` `72-72` cancels out `-9k` `=` `180` `-9k``-:(-9)` `=` `180``-:(-9)` Divide both sides by `-9` `-9``k``-:(-9)` `=` `180``-:(-9)` `times(-9)divide(-9)` cancels out `k` `=` `-20` `k=-20` -
Question 10 of 11
10. Question
Solve for `a``-12(a+11)=-108`- `a=` (-2)
Correct
Exceptional!
Incorrect
To solve for `a`, get `a` by itselfDistribute the value inside the parenthesis.`-12``(a+11)` `=` `-108` `(axx``(-12)``)+(11xx``(-12)``)` `=` `-108` `-12a-132` `=` `-108` Get the `k` variable on one side of the equation`-12a-132` `+132` `=` `-108` `+132` Add `132` to both sides `-12a``-132` `+132` `=` `-108` `+132` `-132+132` cancels out `-12a` `=` `24` `-12a``divide(-12)` `=` `24``divide(-12)` Divide both sides by `-12` `-12``a``divide(-12)` `=` `24``divide(-12)` `times(-12)divide(-12)` cancels out `a` `=` `-2` `a=-2` -
Question 11 of 11
11. Question
Solve`(-(9n-6))/4=-3`- `n=` (2)
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Good Job!
Incorrect
Help VideoInverse Operations
When moving a term to the other side of an equation, the operation is inversed.To solve for `n`, it needs to be alone on one side.Start with removing `1/4` by multiplying both sides of the equation by `4`.$$\frac{-(9\color{#00880A}{n}-6)}{4}$$ `=` `-3` $$\frac{-(9\color{#00880A}{n}-6)}{4}\color{#CC0000}{\times4}$$ `=` `-3``times4` `-(9``n` `-6)` `=` `-12` `1/4 times4` cancels out `-9``n` `+6` `=` `-12` Next, move `6` to the other side by subtracting `6` from both sides of the equation.`-9``n` `+6` `=` `-12` `-9``n` `+6` `-6` `=` `-12` `-6` `-9``n` `=` `-18` `6-6` cancels out Finally, remove `-9` by dividing both sides of the equation by `-9`.`-9``n` `=` `-18` `-9``n``divide-9` `=` `-18``divide-9` `n` `=` `2` `-9divide-9` cancels out Check our workTo confirm our answer, substitute `n=2` to the original equation.`(-(9n-6))/4` `=` `-3` `(-(9(2)-6))/4` `=` `-3` Substitute `n=2` `(-(18-6))/4` `=` `-3` `(-12)/4` `=` `-3` `-3` `=` `-3` Since the equation is true, the answer is correct.`n=2`Hint
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