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Solve Equations with Variables on Both Sides using the Distributive Property>
Solve Equations – Variables on Both Sides (Distributive Property) 1Solve Equations – Variables on Both Sides (Distributive Property) 1
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Question 1 of 4
1. Question
Solve`6(2m+5)-5(3m+2)=26`- `m=` (-2)
Hint
Help VideoCorrect
Great Work!
Incorrect
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` -
Question 2 of 4
2. Question
Solve`8(2y+3)-4(3y+2)=32`- `y=` (4)
Hint
Help VideoCorrect
Well Done!
Incorrect
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 `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` -
Question 3 of 4
3. Question
Solve`9(m+1)=3(m-3)`- `m=` (-3)
Hint
Help VideoCorrect
Good Job!
Incorrect
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.`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` -
Question 4 of 4
4. Question
Solve`2a+5=6(a-4)-3a`- `a=` (29)
Hint
Help VideoCorrect
Good Job!
Incorrect
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 `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`
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