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Solve Equations with Variables on Both Sides using the Distributive Property>
Solve Equations – Variables on Both Sides (Distributive Property) 4Solve Equations – Variables on Both Sides (Distributive Property) 4
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Question 1 of 5
1. Question
Solve for `a``3(2a-4)=4a-6`- `a=` (3)
Hint
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To 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` -
Question 2 of 5
2. Question
Solve for `x``5(2x+7)-6x=8+x`- `x=` (-9)
Hint
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Fantastic!
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To 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` -
Question 3 of 5
3. 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 4 of 5
4. Question
Solve for `x``(3x+1)/5 = (2x-1)/2`- `x=` (7/4)
Hint
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Great Work!
Incorrect
To 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}` -
Question 5 of 5
5. Question
Solve for `x``(x+3)/6-(x-1)/5=1/3`- `x=` (11)
Hint
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Exceptional!
Incorrect
To 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`
Quizzes
- One Step Equations – Add and Subtract 1
- One Step Equations – Add and Subtract 2
- One Step Equations – Add and Subtract 3
- One Step Equations – Add and Subtract 4
- One Step Equations – Multiply and Divide 1
- One Step Equations – Multiply and Divide 2
- One Step Equations – Multiply and Divide 3
- One Step Equations – Multiply and Divide 4
- Two Step Equations 1
- Two Step Equations 2
- Two Step Equations 3
- Two Step Equations 4
- Multi-Step Equations 1
- Multi-Step Equations 2
- Solve Equations using the Distributive Property 1
- Solve Equations using the Distributive Property 2
- Solve Equations using the Distributive Property 3
- Equations with Variables on Both Sides 1
- Equations with Variables on Both Sides 2
- Equations with Variables on Both Sides 3
- Equations with Variables on Both Sides (Fractions) 1
- Equations with Variables on Both Sides (Fractions) 2
- Solve Equations – Variables on Both Sides (Distributive Property) 1
- Solve Equations – Variables on Both Sides (Distributive Property) 2
- Solve Equations – Variables on Both Sides (Distributive Property) 3
- Solve Equations – Variables on Both Sides (Distributive Property) 4
- Writing Equations 1
- Writing Equations 2
- Writing Equations 3
- Writing Equations 4
- Equation Word Problems (Age) 1
- Equation Word Problems (Money) 1
- Equation Word Problems (Harder) 1
- Equation Problems with Substitution 1
- Equation Problems (Geometry) 1
- Equation Problems (Geometry) 2
- Equation Problems (Perimeter)
- Equation Problems (Area)
- Solve for a Variable or Formula 1
- Solve for a Variable or Formula 2
- Solve for a Variable or Formula 3