Distribute completely and keep both sides balanced
Mathematics Knowledge includes high-school mathematics principles. In this selected unit, an equation states that two expressions are equal. A valid solution process keeps them equal by applying equivalent operations to both sides. The distributive property also matters: a factor outside parentheses multiplies each term inside, including a term carrying a minus sign. Worked example: solve 3(x − 4) = x + 10. Distribution gives 3x − 12 = x + 10. Subtract x from each side: 2x − 12 = 10. Add 12 to each side: 2x = 22. Divide both sides by 2: x = 11. The original left side is 3(11 − 4) = 21, and the right side is 11 + 10 = 21, confirming the result. A common incomplete distribution writes 3x − 4 rather than 3x − 12. Another error changes a sign while moving a term but never identifies the equal operation performed on both sides. A safer written line says subtract x from both sides or add 12 to both sides. Once the balance is clear, a compact line of algebra is easier to inspect. Substitution checks the original equation, not merely the last simplified line. An earlier distribution error can produce a consistent answer to a different equation. A correct check should reproduce the same numerical value on both original sides. This unit does not cover every algebra topic in the full ASVAB; it teaches a useful, bounded method for linear equations with the specific operations shown.
What value of x satisfies 4(x − 2) = 2x + 10?
- Distribute first: 4x − 8 = 2x + 10. Subtract 2x from both sides and add 8 to both sides to obtain 2x = 18, so x = 9. Substitution checks both sides: 4(9 − 2) = 28 and 2(9) + 10 = 28.
Compare the other answer choices
This can result from combining the x terms as 6x rather than subtracting equal amounts from both sides.
This can result from moving the −8 with the wrong sign, producing 2x = 2.
This can result from distributing 4 to x but not to −2, yielding 4x − 2 = 2x + 10.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which evidence or rule supports your decision and why the alternatives do not fit.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
ASVAB SubtestsUse a General Strategy to Solve Linear Equations