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Equations with Variables on Both Sides (Fractions) 1Equations with Variables on Both Sides (Fractions) 1
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Question 1 of 5
1. Question
Solve`x+6=5/7 x`- `x=` (-21)
Correct
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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`Get `x` alone to the left side and all constants to the right.Start by removing the fraction by multiplying both sides of the equation by `7`.`x` `+6` `=` `5/7``x` `(``x` `+6)``times7` `=` `5/7``x``times7` `7(``x` `+6)` `=` `5``x` `1/7times7` cancels out Next, expand the left side by using the Distributive Property.`7``(``x` `+6)` `=` `5``x` `7``x` `+``7``(6)` `=` `5``x` `7``x` `+42` `=` `5``x` Next, move `7x` to the other side by subtracting `7x` from both sides of the equation.`7``x` `+42` `=` `5``x` `7``x` `+42` `-7x` `=` `5``x` `-7x` `42` `=` `-2``x` `7x-7x` cancels out Finally, remove `-2` by dividing both sides of the equation by `-2`.`42` `=` `-2``x` `42``divide-2` `=` `-2``x``divide-2` `-21` `=` `x` `-2divide-2` cancels out `x` `=` `-21` Check our workTo confirm our answer, substitute `x=-21` to the original equation.`x+6` `=` `5/7 x` `-21+6` `=` `5/7 (-21)` Substitute `x=-21` `-15` `=` `5(-3)` `-15` `=` `-15` Since the equation is true, the answer is correct.`x=-21` -
Question 2 of 5
2. Question
Solve`(4u)/5+3=u`- `u=` (15)
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Get `u` alone to the left side and all constants to the right.Start by removing the fraction by multiplying both sides of the equation by `5`.$$\frac{4\color{#00880A}{u}}{5}+3$$ `=` `u` $$\left(\frac{4\color{#00880A}{u}}{5}+3\right)\color{#CC0000}{\times5}$$ `=` `u``times5` $$\frac{4\color{#00880A}{u}}{5}\color{#CC0000}{(5)}+3\color{#CC0000}{(5)}$$ `=` `5``u` Distribute `5` to the parenthesis `4``u` `+15` `=` `5``u` `1/5times5` cancels out Next, move `4u` to the other side by subtracting `4u` from both sides of the equation.`4``u` `+15` `=` `5``u` `4``u` `+15` `-4u` `=` `5``u` `-4u` `15` `=` `u` `4u-4u` cancels out `u` `=` `15` Check our workTo confirm our answer, substitute `u=15` to the original equation.`(4u)/5+3` `=` `u` `(4(15))/5+3` `=` `15` Substitute `u=15` `60/5+3` `=` `15` `12+3` `=` `15` `15` `=` `15` Since the equation is true, the answer is correct.`u=15` -
Question 3 of 5
3. Question
Solve`7x=(5x-8)/3`- `x=` (-1/2)
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Inverse Operations
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 removing the fraction by multiplying both sides of the equation by `3`.`7``x` `=` $$\frac{5\color{#00880A}{x}-8}{3}$$ `7``x``times3` `=` $$\frac{5\color{#00880A}{x}-8}{3}\color{#CC0000}{\times3}$$ `21``x` `=` `5``x` `-8` `1/3times3` cancels out Next, move `5x` to the other side by subtracting `5x` from both sides of the equation.`21``x` `=` `5``x` `-8` `21``x` `-5x` `=` `5``x` `-8` `-5x` `16``x` `=` `-8` `5x-5x` cancels out Finally, remove `16` by dividing both sides of the equation by `16`.`16``x` `=` `-8` `16``x``divide16` `=` `-8``divide16` `x` `=` `-1/2` `16divide16` cancels out Check our workTo confirm our answer, substitute `x=-1/2` to the original equation.`7x` `=` `(5x-8)/3` `7(-1/2)` `=` `[5(-1/2)-8]/3` Substitute `x=-1/2` `-7/2` `=` `[-5/2-8]/3` `-7/2` `=` `[-21/2]/3` `-7/2` `=` `-21/2 times 1/3` `-7/2` `=` `-21/6` `-7/2` `=` `-7/2` Since the equation is true, the answer is correct.`x=-1/2` -
Question 4 of 5
4. Question
Solve for `t``3t-2=3/5 t+1`Hint
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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`Get `t` alone to the left side and all constants to the right.Start by removing the fraction by multiplying both sides of the equation by `5`, then using the Distributive Property.`3``t` `-2` `=` `3/5``t` `+1` `(3``t` `-2)``times5` `=` $$\left(\frac{3}{5}\color{#00880A}{t}+1\right)\color{#CC0000}{\times5}$$ `5``(3``t` `-2)` `=` $$\color{#007DDC}{5}\left(\frac{3}{5}\color{#00880A}{t}+1\right)$$ `5``(3``t``)+``5``(-2)` `=` $$\color{#007DDC}{5}\left(\frac{3}{5}\color{#00880A}{t}\right)+\color{#007DDC}{5}(1)$$ `15``t` `-10` `=` `3``t` `+5` `1/5times5` cancels out Next, move `-10` to the other side by adding `10` to both sides of the equation.`15``t` `-10` `=` `3``t` `+5` `15``t` `-10` `+10` `=` `3``t` `+5` `+10` `15``t` `=` `3``t` `+15` `-10+10` cancels out Now, move `3t` to the other side by subtracting `3t` from both sides of the equation.`15``t` `=` `3``t` `+15` `15``t` `-3t` `=` `3``t` `+15` `-3t` `12``t` `=` `15` `3t-3t` cancels out Finally, remove `12` by dividing both sides of the equation by `12`.`12``t` `=` `15` `12``t``divide12` `=` `15``divide12` `t` `=` `15/12` `12divide12` cancels out `t` `=` `5/4` Simplify the fraction `t` `=` `1 1/4` Check our workTo confirm our answer, substitute `t=1 1/4` or `t=5/4` to the original equation.`3t-2` `=` `3/5 t+1` `3(5/4)-2` `=` `3/5 (5/4)+1` Substitute `x=5/4` `15/4-2` `=` `15/20+1` `(15-8)/4` `=` `(15+20)/20` `7/4` `=` `35/20` `7/4` `=` `7/4` Since the equation is true, the answer is correct.`x=1 1/4` -
Question 5 of 5
5. Question
Solve for `x``x/4-x/5=12`- `x=` (240)
Hint
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To solve for `x`, get `x` by itself`4` and `5` has `20` as a common denominatorMake sure that fractions have the common denominator which is `20``frac{x}{4}-frac{x}{5}` `=` `12` `frac{x}{4}``timesfrac{5}{5}``-frac{x}{5}``timesfrac{4}{4}` `=` `12` `frac{5x}{20}-frac{4x}{20}` `=` `12` Combine the fractions and find the value of `x``frac{5x-4x}{20}` `=` `12` `frac{x}{20}` `=` `12` `frac{x}{20}``times20` `=` `12``times20` Multiply both sides by `20` `frac{20x}{20}` `=` `12``times20` `x` `=` `240` The coefficient `frac{20}{20}` cancels out `x=240`
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