Math · Original worked example
Distribute to every term inside the parentheses
Learn to distribute positive and negative factors, solve an equation, and check your answer with an original ACT-style example.
Before you begin
Useful foundation: Multiply signed numbers and combine like terms.
Your goal: Expand an expression without dropping a term or changing a sign.
In a(b + c), the outside factor multiplies both terms: ab + ac. Treat a subtraction as adding a negative term.
Work through an example
Solve 3(x + 2) − 4 = 17.
- Distribute the 3: 3x + 6 − 4 = 17. Both x and 2 are multiplied by 3.
- Combine constants: 3x + 2 = 17.
- Subtract 2 from both sides: 3x = 15. Divide both sides by 3: x = 5.
- Check in the original equation: 3(5 + 2) − 4 = 21 − 4 = 17.
Try a question yourself
Choose an answer, then check your reasoning. This public practice is not saved.
Read all answer explanations
−5x + 10 — correct answer: Yes. −2 × 3x = −6x and −2 × (−5) = +10. Adding x gives −5x + 10.
−7x + 10: The constant is right, but −6x + x = −5x, not −7x.
−5x − 10: The x terms are right. The constant is positive because a negative times a negative is positive.
−6x + 5: Distribute to both terms, then include the final +x. The products are −6x and +10.
What to do next
Try an equation with parentheses on both sides, then check your solution by substitution.
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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Browse all four subjects →These original practice examples are independent of ACT and are not official test questions.