Back to Equations
Equations with Variables on Both Sides
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Question 1 of 15
1. Question
Solve`3a+4=2a+10`- `a=` (6)
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Get `a` alone to the left side and all constants to the right.Start by moving `4` to the other side by subtracting `4` from both sides of the equation.`3``a` `+4` `=` `2``a` `+10` `3``a` `+4` `-4` `=` `2``a` `+10` `-4` `3``a` `=` `2``a` `+6` `4-4` cancels out Next, move `2a` to the other side by subtracting `2a` from both sides of the equation.`3``a` `=` `2``a` `+6` `3``a` `-2a` `=` `2``a` `+6` `-2a` `a` `=` `6` `2a-2a` cancels out Check our workTo confirm our answer, substitute `a=6` to the original equation.`3a+4` `=` `2a+10` `3(6)+4` `=` `2(6)+10` Substitute `a=6` `18+4` `=` `12+10` `22` `=` `22` Since the equation is true, the answer is correct.`a=6`Hint
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Question 2 of 15
2. Question
Solve`4m-3=24+m`- `m=` (9)
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When moving a term to the other side of an equation, the operation is inversed.Get `m` alone to the left side and all constants to the right.Start by moving `-3` to the other side by adding `3` to both sides of the equation.`4``m` `-3` `=` `24+` `m` `4``m` `-3` `+3` `=` `24+` `m` `+3` `4``m` `=` `27+` `m` `-3+3` cancels out Next, move `m` to the other side by subtracting `m` from both sides of the equation.`4``m` `=` `27+` `m` `4``m` `-m` `=` `27+` `m` `-m` `3``m` `=` `27` `m-m` cancels out Finally, remove `3` by dividing `3` from both sides.`3``m` `=` `27` `3``m``-:3` `=` `27``-:3` `m` `=` `9` `3-:3` cancels out Check our workTo confirm our answer, substitute `m=9` to the original equation.`4m-3` `=` `24+m` `4(9)-3` `=` `24+9` Substitute `m=9` `36-3` `=` `33` `33` `=` `33` Since the equation is true, the answer is correct.`m=9`Hint
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Question 3 of 15
3. Question
Solve`8y-2=6y+28`- `y=` (15)
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When moving a term to the other side of an equation, the operation is inversed.Get `y` alone to the left side and all constants to the right.Start by moving `-2` to the other side by adding `2` to both sides of the equation.`8``y` `-2` `=` `6``y` `+28` `8``y` `-2` `+2` `=` `6``y` `+28` `+2` `8``y` `=` `6``y` `+30` `-2+2` cancels out Next, move `6y` to the other side by subtracting `6y` from both sides of the equation.`8``y` `=` `6``y` `+30` `8``y` `-6y` `=` `6``y` `+30` `-6y` `2``y` `=` `30` `6y-6y` cancels out Finally, remove `2` by dividing `2` from both sides.`2``y` `=` `30` `2``y``divide2` `=` `30``divide2` `y` `=` `15` `2-:2` cancels out Check our workTo confirm our answer, substitute `y=15` to the original equation.`8y-2` `=` `6y+28` `8(15)-2` `=` `6(15)+28` Substitute `y=15` `120-2` `=` `90+28` `118` `=` `118` Since the equation is true, the answer is correct.`y=15`Hint
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Question 4 of 15
4. Question
Solve`n+5=13-n`- `n=` (4)
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When moving a term to the other side of an equation, the operation is inversed.Get `n` alone to the left side and all constants to the right.Start by moving `5` to the other side by subtracting `5` from both sides of the equation.`n` `+5` `=` `13-``n` `n` `+5` `-5` `=` `13-``n` `-5` `n` `=` `8-``n` `5-5` cancels out Next, move `-n` to the other side by adding `n` to both sides of the equation.`n` `=` `8-``n` `n` `+n` `=` `8-``n` `+n` `2``n` `=` `8` `-n+n` cancels out Finally, remove `2` by dividing `2` from both sides.`2``n` `=` `8` `2``n``divide2` `=` `8``divide2` `n` `=` `4` `2-:2` cancels out Check our workTo confirm our answer, substitute `n=4` to the original equation.`n+5` `=` `13-n` `4+5` `=` `13-4` Substitute `n=4` `9` `=` `9` Since the equation is true, the answer is correct.`n=4`Hint
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Question 5 of 15
5. Question
Solve`6y-4=7y+10`- `y=` (-14)
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Keep Going!
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Help VideoInverse Operations
When moving a term to the other side of an equation, the operation is inversed.Get `y` alone to the left side and all constants to the right.Start by moving `10` to the other side by subtracting `10` from both sides of the equation.`6``y` `-4` `=` `7``y` `+10` `6``y` `-4` `-10` `=` `7``y` `+10` `-10` `6``y` `-14` `=` `7``y` `10-10` cancels out Next, move `6y` to the other side by subtracting `6y` from both sides of the equation.`6``y` `-14` `=` `7``y` `6``y` `-14` `-6y` `=` `7``y` `-6y` `-14` `=` `y` `6y-6y` cancels out `y` `=` `-14` Check our workTo confirm our answer, substitute `y=-14` to the original equation.`6y-4` `=` `7y+10` `6(-14)-4` `=` `7(-14)+10` Substitute `y=-14` `-84-4` `=` `-98+10` `-88` `=` `-88` Since the equation is true, the answer is correct.`y=-14`Hint
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Question 6 of 15
6. Question
Solve`12x-8=18x-5`Write fractions as “a/b”- `x=` (-1/2)
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When moving a term to the other side of an equation, the operation is inversed.Get `x` alone to the left side and all constants to the right.Start by moving `-5` to the other side by adding `5` to both sides of the equation.`12``x` `-8` `=` `18``x` `-5` `12``x` `-8` `+5` `=` `18``x` `-5` `+5` `12``x` `-3` `=` `18``x` `-5+5` cancels out Next, move `12x` to the other side by subtracting `12x` from both sides of the equation.`12``x` `-3` `=` `18``x` `12``x` `-3` `-12x` `=` `18``x` `-12x` `-3` `=` `6``x` `12x-12x` cancels out Finally, remove `6` by dividing both sides of the equation by `6`.`-3` `=` `6``x` `-3``divide6` `=` `6``x``divide6` `-1/2` `=` `x` `6divide6` cancels out `x` `=` `-1/2` Check our workTo confirm our answer, substitute `x=-1/2` to the original equation.`12x-8` `=` `18x-5` `12(-1/2)-8` `=` `18(-1/2)-5` Substitute `x=-1/2` `-6-8` `=` `-9-5` `-14` `=` `-14` Since the equation is true, the answer is correct.`x=-1/2`Hint
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Question 7 of 15
7. Question
Solve`2y+19=-5y+33`- `y=` (2)
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When moving a term to the other side of an equation, the operation is inversed.Get `y` alone to the left side and all constants to the right.Start by moving `19` to the other side by subtracting `19` from both sides of the equation.`2``y` `+19` `=` `-5``y` `+33` `2``y` `+19` `-19` `=` `-5``y` `+33` `-19` `2``y` `=` `-5``y` `+14` `19-19` cancels out Next, move `-5y` to the other side by adding `5y` to both sides of the equation.`2``y` `=` `-5``y` `+14` `2``y` `+5y` `=` `-5``y` `+14` `+5y` `7``y` `=` `14` `-5y+5y` cancels out Finally, remove `7` by dividing both sides of the equation by `7`.`7``y` `=` `14` `7``y``divide7` `=` `14``divide7` `y` `=` `2` `7divide7` cancels out Check our workTo confirm our answer, substitute `y=2` to the original equation.`2y+19` `=` `-5y+33` `2(2)+19` `=` `-5(2)+33` Substitute `y=2` `4+19` `=` `-10+33` `23` `=` `23` Since the equation is true, the answer is correct.`y=2`Hint
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Question 8 of 15
8. Question
Solve`6-3r=8-r`- `r=` (-1)
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When moving a term to the other side of an equation, the operation is inversed.Get `r` alone to the left side and all constants to the right.Start by moving `6` to the other side by subtracting `6` from both sides of the equation.`6-3``r` `=` `8-``r` `6-3``r` `-6` `=` `8-``r` `-6` `-3``r` `=` `2-``r` `6-6` cancels out Next, move `-r` to the other side by adding `r` to both sides of the equation.`-3``r` `=` `2-``r` `-3``r` `+r` `=` `2-``r` `+r` `-2``r` `=` `2` `-r+r` cancels out Finally, remove `-2` by dividing both sides of the equation by `-2`.`-2``r` `=` `2` `-2``r``divide-2` `=` `2``divide-2` `r` `=` `-1` `-2divide-2` cancels out Check our workTo confirm our answer, substitute `r=-1` to the original equation.`6-3r` `=` `8-r` `6-3(-1)` `=` `8-(-1)` Substitute `r=-1` `6+3` `=` `8+1` `9` `=` `9` Since the equation is true, the answer is correct.`r=-1`Hint
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Question 9 of 15
9. Question
Solve for `x``10x-5=x+4`- `x=` (1)
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Well Done!
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Help VideoTo solve for `x`, get `x` by itselfSubtract `x` from both sides of the equation`10x-5` `-x` `=` `x+4` `-x` `10x-5` `-x` `=` `x``+4` `-x` `x-x` cancels out `9x-5` `=` `4` Next, add `5` to both sides of the equation`9x-5` `+5` `=` `4` `+5` `9x``-5` `+5` `=` `4` `+5` `-5+5` cancels out `9x` `=` `9` Finally, divide both sides of the equation by `9``9x``divide9` `=` `9``divide9` `9``x``divide9` `=` `9``divide9` `times9divide9` cancels out `x` `=` `1` `x=1`Hint
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Question 10 of 15
10. Question
Solve for `x``4x+5=-8x-7`- `x=` (-1)
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Help VideoTo solve for `x`, get `x` by itselfAdd `8x` to both sides of the equation`4x+5` `+8x` `=` `-8x-7` `+8x` `4x+5` `+8x` `=` `-8x``-7` `+8x` `-8x+8x` cancels out `12x+5` `=` `-7` Next, subtract `5` from both sides of the equation`12x+5` `-5` `=` `-7` `-5` `12x``+5` `-5` `=` `-7` `-5` `5-5` cancels out `12x` `=` `-12` Finally, divide both sides of the equation by `12``12x``divide12` `=` `-12``divide12` `12``x``divide12` `=` `-12``divide12` `times12divide12` cancels out `x` `=` `-1` `x=-1`Hint
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Question 11 of 15
11. Question
Solve for `x``3x+2=2x+9`- `x=` (7)
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Help VideoTo solve for `x`, get `x` by itselfSubtract `2x` from both sides of the equation`3x+2` `-2x` `=` `2x+9` `-2x` `3x+2` `-2x` `=` `2x``+9` `-2x` `2x-2x` cancels out `x+2` `=` `9` Finally, subtract `2` from both sides of the equation`x+2` `-2` `=` `9` `-2` `x``+2` `-2` `=` `9` `-2` `2-2` cancels out `x` `=` `7` `x=7`Hint
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Question 12 of 15
12. Question
Solve for `x``3x+5=2x+7`- `x=` (2)
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Fantastic!
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Help VideoTo solve for `x`, get `x` by itselfSubtract `2x` from both sides of the equation`3x+5` `-2x` `=` `2x+7` `-2x` `3x+5` `-2x` `=` `2x``+7` `-2x` `2x-2x` cancels out `x+5` `=` `7` Finally, subtract `5` from both sides of the equation`x+5` `-5` `=` `7` `-5` `x``+5` `-5` `=` `7` `-5` `5-5` cancels out `x` `=` `2` `x=2`Hint
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Question 13 of 15
13. Question
Solve for `p``p-5+3p=-9`- `p=` (-1)
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To solve for `p`, get `p` by itselfCombine like terms to simplify.`p` `-5``+3p` `=` `-9` `(p+3p)` `-5` `=` `-9` `4p-5` `=` `-9` Add `5` to both sides of the equation`4p-5` `+5` `=` `-9` `+5` `4p``-5` `+5` `=` `-9` `+5` `-5+5` cancels out `4p` `=` `-4` `4p``divide4` `=` `-4``divide4` Divide both sides by `4` `4``p``divide4` `=` `-4``divide4` `times4divide4` cancels out `p` `=` `-1` `p=-1` -
Question 14 of 15
14. Question
Solve for `r``-12=-2r-4r`- `r=` (2)
Correct
Correct!
Incorrect
To solve for `r`, get `r` by itselfCombine like terms to simplify.`-12` `=` `-2r-4r` `-12` `=` `-6r` Get the `r` variable on one side of the equation`-12``divide(-6)` `=` `-6r``divide(-6)` Divide both sides by `-6` `-12``divide(-6)` `=` `-6``r``divide(-6)` `times(-6)divide(-6)` cancels out `2` `=` `r` `r` `=` `2` `r=2` -
Question 15 of 15
15. Question
Solve for `a``8a-7=5a-4`- `a=` (1)
Correct
Great Work!
Incorrect
Help VideoTo solve for `a`, get `a` by itselfSubtract `5a` from both sides of the equation`8a-7` `-5a` `=` `5a-4` `-5a` `8a-7` `-5a` `=` `5a``-4` `-5a` `5a-5a` cancels out `3a-7` `=` `-4` Next, add `7` to both sides of the equation`3a-7` `+7` `=` `-4` `+7` `3a``-7` `+7` `=` `-4` `+7` `-7+7` cancels out `3a` `=` `3` Finally, divide both sides of the equation by `3``3a``divide3` `=` `3``divide3` `3``a``divide3` `=` `3``divide3` `times3divide3` cancels out `a` `=` `1` `a=1`Hint
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