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Equations with Variables on Both Sides (Fractions) 2Equations with Variables on Both Sides (Fractions) 2
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Question 1 of 5
1. Question
Solve`(x-1)/5=(x+5)/2`- `x=` (-9)
Hint
Help VideoCorrect
Excellent!
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`Get `x` alone to the left side and all constants to the right.First, remove the fractions by finding the Least Common Denominator `(LCD)` of the denominators `5` and `2`.Multiples of `5`:`5` `10` `15 20 25`Multiples of `2`:`2 4 6 8` `10`The `LCD` of `5` and `2` is `10`Multiply the `LCD` to both sides of the equation to remove the fractions.$$\frac{\color{#00880A}{x}-1}{5}\color{#D800AD}{\times10}$$ `=` $$\frac{\color{#00880A}{x}+5}{2}\color{#D800AD}{\times10}$$ $$\frac{10(\color{#00880A}{x}-1)}{5}$$ `=` $$\frac{10(\color{#00880A}{x}+5)}{2}$$ `2``(``x` `-1)` `=` `5``(``x` `+5)` Divide `10` by each denominator `2``(``x``)-``2``(1)` `=` `5``(``x``)+``5``(5)` Distribute the constants inside the parentheses `2``x` `-2` `=` `5``x` `+25` Simplify Next, move `5x` to the other side by subtracting `5x` from both sides of the equation.`2``x` `-2` `=` `5``x` `+25` `2``x` `-2` `-5x` `=` `5``x` `+25` `-5x` `-3``x` `-2` `=` `25` `5x-5x` cancels out Then, move `-2` to the other side by adding `2` to both sides of the equation.`-3``x` `-2` `=` `25` `-3``x` `-2` `+2` `=` `25` `+2` `-3``x` `=` `27` `-2+2` cancels out Finally, remove `-3` by dividing both sides of the equation by `-3`.`-3``x` `=` `27` `-3``x``divide-3` `=` `27``divide-3` `x` `=` `-9` `-3divide-3` cancels out Check our workTo confirm our answer, substitute `x=-9` to the original equation.`(x-1)/5` `=` `(x+5)/2` `(-9-1)/5` `=` `(-9+5)/2` Substitute `x=-9` `(-10)/5` `=` `(-4)/2` `-2` `=` `-2` Since the equation is true, the answer is correct.`x=-9` -
Question 2 of 5
2. Question
Solve for `a``(3a)/5 + a/2 = 4`- `a=` (40/11)
Hint
Help VideoCorrect
Great Work!
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To solve for `a`, get `a` by itself`5` and `2` has `10` as a common denominatorMake sure that fractions have the common denominator which is `10``frac{3a}{5}+frac{a}{2}` `=` `4` `frac{3a}{5}``timesfrac{2}{2}``+frac{a}{2}``timesfrac{5}{5}` `=` `4` `frac{6a}{10}+frac{5a}{10}` `=` `4` Combine the fractions and find the value of `x``frac{6a+5a}{10}` `=` `4` `frac{11a}{10}` `=` `4` `frac{11a}{10}``times10` `=` `4``times10` Multiply both sides by `10` `frac{10(11a)}{10}` `=` `4``times10` `11a` `=` `40` The coefficient `frac{10}{10}` cancels out `11a``divide11` `=` `40``divide11` Divide both sides by `11` `11``a``divide11` `=` `40``divide11` `times11divide11` cancels out `a` `=` `40/11` `a=40/11` -
Question 3 of 5
3. Question
Solve`3+2/3 y=4+1/2 y`- `y=` (6)
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`Get `y` alone to the left side and all constants to the right.First, remove the fractions by finding the Least Common Denominator `(LCD)` of the denominators `3` and `2`.Multiples of `3`:`3` `6` `9 12 15`Multiples of `2`:`2 4` `6` `8 10`The `LCD` of `3` and `2` is `6`Multiply the `LCD` to both sides of the equation to remove the fractions. Use the Distributive Property.$$\left(3+\frac{2}{3}\color{#00880A}{y}\right)\color{#D800AD}{\times6}$$ `=` $$\left(4+\frac{1}{2}\color{#00880A}{y}\right)\color{#D800AD}{\times6}$$ $$\color{#007DDC}{6}\left(3+\frac{2}{3}\color{#00880A}{y}\right)$$ `=` $$\color{#007DDC}{6}\left(4+\frac{1}{2}\color{#00880A}{y}\right)$$ $$\color{#007DDC}{6}(3)+\color{#007DDC}{6}\left(\frac{2}{3}\color{#00880A}{y}\right)$$ `=` $$\color{#007DDC}{6}(4)+\color{#007DDC}{6}\left(\frac{1}{2}\color{#00880A}{y}\right)$$ $$18+\frac{12}{3}\color{#00880A}{y}$$ `=` $$24+\frac{6}{2}\color{#00880A}{y}$$ `18+4``y` `=` `24+3``y` Simplify Next, move `3y` to the other side by subtracting `3y` from both sides of the equation.`18+4``y` `=` `24+3``y` `18+4``y` `-3y` `=` `24+3``y` `-3y` `18+``y` `=` `24` `3y-3y` cancels out Finally, move `18` to the other side by subtracting `18` from both sides of the equation.`18+``y` `=` `24` `18+``y` `-18` `=` `24` `-18` `y` `=` `6` `18-18` cancels out Check our workTo confirm our answer, substitute `y=6` to the original equation.`3+2/3 y` `=` `4+1/2 y` `3+2/3 (6)` `=` `4+1/2 (6)` Substitute `y=6` `3+12/3` `=` `4+6/2` `3+4` `=` `4+3` `7` `=` `7` Since the equation is true, the answer is correct.`y=6` -
Question 4 of 5
4. Question
Solve`1/4 m-2=1/3 m+4`- `m=` (-72)
Hint
Help VideoCorrect
Excellent!
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`Get `m` alone to the left side and all constants to the right.First, remove the fractions by finding the Least Common Denominator `(LCD)` of the denominators `4` and `3`.Multiples of `4`:`4 8` `12` `16 20`Multiples of `3`:`3 6 9` `12` `15`The `LCD` of `4` and `3` is `12`Multiply the `LCD` to both sides of the equation to remove the fractions. Use the Distributive Property.$$\left(\frac{1}{4}\color{#00880A}{m}-2\right)\color{#D800AD}{\times12}$$ `=` $$\left(\frac{1}{3}\color{#00880A}{m}+4\right)\color{#D800AD}{\times12}$$ $$\color{#007DDC}{12}\left(\frac{1}{4}\color{#00880A}{m}-2\right)$$ `=` $$\color{#007DDC}{12}\left(\frac{1}{3}\color{#00880A}{m}+4\right)$$ $$\color{#007DDC}{12}\left(\frac{1}{4}\color{#00880A}{m}\right)+\color{#007DDC}{12}(-2)$$ `=` $$\color{#007DDC}{12}\left(\frac{1}{3}\color{#00880A}{m}\right)+\color{#007DDC}{12}(4)$$ $$\frac{12}{4}\color{#00880A}{m}-24$$ `=` $$\frac{12}{3}\color{#00880A}{m}+48$$ `3``m` `-24` `=` `4``m` `+48` Simplify Next, move `3m` to the other side by subtracting `3m` from both sides of the equation.`3``m` `-24` `=` `4``m` `+48` `3``m` `-24` `-3m` `=` `4``m` `+48` `-3m` `-24` `=` `m` `+48` `3m-3m` cancels out Finally, move `48` to the other side by subtracting `48` from both sides of the equation.`-24` `=` `m` `+48` `-24` `-48` `=` `m` `+48` `-48` `-72` `=` `m` `48-48` cancels out `m` `=` `-72` Check our workTo confirm our answer, substitute `m=-72` to the original equation.`1/4 m-2` `=` `1/3 m+4` `1/4 (-72)-2` `=` `1/3 (-72)+4` Substitute `m=-72` `(-72)/4 -2` `=` `(-72)/3 +4` `-18-2` `=` `-24+4` `-20` `=` `-20` Since the equation is true, the answer is correct.`m=-72` -
Question 5 of 5
5. Question
Solve`(6x-3)/5=(5x+3)/6`- `x=` (3)
Hint
Help VideoCorrect
Well Done!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Cross Product
Distributive Property
`a``(b+c)=``a``b+``a``c`Get `x` alone to the left side and all constants to the right.First, remove the fractions by using the Cross Product.$$\frac{6\color{#00880A}{x}-3}{5}$$ `=` $$\frac{5\color{#00880A}{x}+3}{6}$$ `6(6``x` `-3)` `=` `5(5``x` `+3)` Expand both sides of the equation by using the Distributive Property.`6``(6``x` `-3)` `=` `5``(5``x` `+3)` `6``(6``x``)-``6``(3)` `=` `5``(5``x``)+``5``(3)` `36``x``-18` `=` `25``x``+15` Next, move `-18` to the other side by adding `18` to both sides of the equation.`36``x``-18` `=` `25``x``+15` `36``x``-18` `+18` `=` `25``x``+15` `+18` `36``x` `=` `25``x` `+33` `-18+18` cancels out Then, move `25x` to the other side by subtracting `25x` from both sides of the equation.`36``x` `=` `25``x` `+33` `36``x` `-25x` `=` `25``x` `+33` `-25x` `11``x` `=` `33` `25x-25x` cancels out Finally, remove `11` by dividing both sides of the equation by `11`.`11``x` `=` `33` `11``x``-:11` `=` `33``-:11` `x` `=` `3` `11divide11` cancels out Check our workTo confirm our answer, substitute `x=3` to the original equation.`(6x-3)/5` `=` `(5x+3)/6` `(6(3)-3)/5` `=` `(5(3)+3)/6` Substitute `x=3` `(18-3)/5` `=` `(15+3)/6` `15/5` `=` `18/6` `3` `=` `3` Since the equation is true, the answer is correct.`x=3`
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