Equations with Variables on Both Sides

This worksheet helps sixth-grade students practice solving linear equations with variables on both sides, building foundational algebra skills.

Grade 6 Math AlgebraEquations with Variables on Both Sides

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Includes

Multiple ChoiceFill in the Blanks2 Short AnswerTrue / FalseCustom

Standards

CCSS.MATH.CONTENT.6.EE.B.5CCSS.MATH.CONTENT.6.EE.B.7

Topics

mathalgebraequationsvariablesgrade 6

8 sections · Free to use · Printable

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Equations with Variables on Both Sides

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Read each question carefully and solve for the variable. Show your work for each problem.

1. Which operation should be performed first to solve 3x + 5 = x + 15?

Add 5 to both sides

Subtract x from both sides

Multiply both sides by 3

Divide both sides by 3

2. If 2y - 7 = 5y + 2, what is the value of y?

y = 3

y = -3

y = 9

y = -9

3. To solve an equation with variables on both sides, you should first try to gather all the variable terms on one side of the .

4. The goal of solving an equation is to isolate the .

5. Solve for m: 4m + 8 = 2m + 20

6. Solve for p: 7p - 10 = 3p + 6

7. When solving 5x - 3 = 2x + 9, it is always best to move the smaller variable term first.

True

False

8. The equation 6a + 1 = 6a - 5 has no solution.

True

False

9. Sarah and Tom are saving money. Sarah starts with $20 and saves $5 each week. Tom starts with $10 and saves $7 each week. In how many weeks will they have the same amount of money? Write and solve an equation.

10. The image below represents an equation. If each 'x' represents a variable and each square represents a unit of 1, write the equation and solve for x.