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Equations with Variables on Both Sides>
Equations with Variables on Both Sides 3Equations with Variables on Both Sides 3
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Question 1 of 5
1. Question
Solve`6y-4=7y+10`- `y=` (-14)
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Inverse 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` -
Question 2 of 5
2. Question
Solve`12x-8=18x-5`Write fractions as “a/b”- `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 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` -
Question 3 of 5
3. Question
Solve`2y+19=-5y+33`- `y=` (2)
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Inverse 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 `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` -
Question 4 of 5
4. Question
Solve`6-3r=8-r`- `r=` (-1)
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Inverse Operations
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` -
Question 5 of 5
5. Question
Solve for `a``8a-7=5a-4`- `a=` (1)
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To 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`
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