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Math · Original worked example

Solve equations with variables on both sides

Solve an original linear equation step by step, keep both sides balanced, and verify your answer by substitution before trying a new problem.

By Raise Your ACT · Updated October 27, 2026 · How we review content

Before you begin

Useful foundation: Combine like terms and add, subtract, multiply, and divide signed numbers.

Your goal: Isolate the variable while preserving equality, then check the result in the original equation.

Perform the same operation on both sides. Move variable terms to one side and constants to the other; divide only after the variable terms have been combined.

Work through an example

Solve 7x − 9 = 3x + 15.
  1. Subtract 3x from both sides: 4x − 9 = 15. Subtracting the same quantity keeps the equation balanced.
  2. Add 9 to both sides: 4x = 24. The −9 and +9 cancel on the left.
  3. Divide both sides by 4: x = 6.
  4. Check: 7(6) − 9 = 33 and 3(6) + 15 = 33. Both sides have the same value.

Try a question yourself

What value of x satisfies 5x + 8 = 2x − 13?

Choose an answer, then check your reasoning. This public practice is not saved.

Read all answer explanations

−7 — correct answer: Subtract 2x and then 8 from both sides: 3x = −21, so x = −7. Substitution gives −27 on both sides.

7: The constants give −13 − 8 = −21, not +21. With x = 7, the two sides would be 43 and 1.

−21: −21 is the value of 3x after combining terms. Divide by 3 to find x itself.

−5/3: This comes from combining −13 and +8. To cancel +8 on the left, subtract 8 from both sides, giving −13 − 8 on the right.

What to do next

Explain each balancing operation aloud, then try an equation with parentheses. Check your result before working on speed.

Revisit the idea in a week using a different question. Repeating this example can help you understand it, but remembering its answer is not evidence of learning a new problem.

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These original practice examples are independent of ACT and are not official test questions.