Free sample activity · Grades 6–8
Linear Equations Practice
Practice one-variable equations after working with inverse operations and signed numbers. This short set includes equations with variables on both sides; it does not cover graphs or systems of equations.
6 questions · No account · No timer · Immediate feedback
Before you begin
How to use this activity
Allow five to ten minutes. Write each step, apply the same operation to both sides, and substitute your answer into the original equation.
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Put it into practice
Choose an answer, read the explanation, then move to the next question. Your answers stay in this page and are not saved.
Solve x + 7 = 19. What is x?
Subtract 7 from both sides: x = 19 - 7 = 12. Check: 12 + 7 = 19.
Solve 4x = 28. What is x?
Divide both sides by 4: x = 7. Substituting gives 4 × 7 = 28.
Solve 3x - 5 = 16. What is x?
Add 5 to both sides to get 3x = 21, then divide by 3. The solution is x = 7.
Solve x/4 + 2 = 5. What is x?
Subtract 2 to get x/4 = 3. Multiply both sides by 4 to get x = 12.
Solve 3x + 2 = x + 10. What is x?
Subtract x and then 2 from both sides: 2x = 8, so x = 4. Both sides of the original equation then equal 14.
Solve -2x = 10. What is x?
Divide both sides by -2 to get x = -5. Check: -2 × -5 = 10.
Practice complete
Write an equation whose solution is a negative number. Solve it in two different ways and check both solutions by substitution.
Review every answer and explanation below, or try the activity again.
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Keep the reasoning
All questions, answers & explanations
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Undoing addition
Solve x + 7 = 19. What is x?
Answer: 12
Subtract 7 from both sides: x = 19 - 7 = 12. Check: 12 + 7 = 19.
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Undoing multiplication
Solve 4x = 28. What is x?
Answer: 7
Divide both sides by 4: x = 7. Substituting gives 4 × 7 = 28.
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Two steps
Solve 3x - 5 = 16. What is x?
Answer: 7
Add 5 to both sides to get 3x = 21, then divide by 3. The solution is x = 7.
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Division in an equation
Solve x/4 + 2 = 5. What is x?
Answer: 12
Subtract 2 to get x/4 = 3. Multiply both sides by 4 to get x = 12.
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Variables on both sides
Solve 3x + 2 = x + 10. What is x?
Answer: 4
Subtract x and then 2 from both sides: 2x = 8, so x = 4. Both sides of the original equation then equal 14.
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A negative solution
Solve -2x = 10. What is x?
Answer: -5
Divide both sides by -2 to get x = -5. Check: -2 × -5 = 10.
Take it one step further
Write an equation whose solution is a negative number. Solve it in two different ways and check both solutions by substitution.
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