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ASVAB · Algebra Basics and Equations

Simplify: 4(2x + 3) − 2(x − 5)

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Correct answer

6x + 22

  1. A 6x + 2
  2. B 6x + 22
  3. C 8x + 17
  4. D 10x + 7

Why this is the answer

Distribute each coefficient through its parentheses, watching signs. 4(2x + 3) = 8x + 12. −2(x − 5) = −2x + 10 (note: −2 times −5 = +10). Combine: 8x + 12 − 2x + 10. Combine like terms: (8x − 2x) + (12 + 10) = 6x + 22. The most common error is sign mistakes when distributing a negative coefficient — −2(x − 5) is −2·x + (−2)·(−5) = −2x + 10, NOT −2x − 10. Always distribute the sign with the coefficient. Like terms (terms with the same variable raised to the same power) can be combined; constants are like terms with each other; x terms are like terms with each other.
Source: ASVAB Math Knowledge — Simplifying Expressions

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About this topic: Algebra Basics and Equations

Algebra basics cover solving linear equations and inequalities, working with expressions, substitution and simple systems. Do the same operation to both sides, and check your answer by substituting it back. This is one of 17 Mathematics Knowledge questions on algebra basics and equations, each with a full explanation on a single study page.

New to this exam? Our ASVAB exam guide explains the format, scoring, and how to prepare.

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