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.
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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.
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