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ASVAB · Algebra Basics and Equations

Solve for x: 3x + 7 = 22

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Correct answer

x = 5

  1. A x = 5
  2. B x = 7
  3. C x = 15
  4. D x = 3

Why this is the answer

Linear equation solving: isolate the variable. Step 1: subtract 7 from both sides: 3x + 7 − 7 = 22 − 7, giving 3x = 15. Step 2: divide both sides by 3: 3x ÷ 3 = 15 ÷ 3, giving x = 5. Verify: 3(5) + 7 = 15 + 7 = 22 ✓. The two-step linear equation is the foundation of algebra. Strategy: undo operations in reverse order of operations — first reverse addition/subtraction, then reverse multiplication/division. Many ASVAB MK problems use this structure. Common errors: dividing before subtracting; sign errors; arithmetic errors. Always verify by substituting the answer back into the original equation. Linear equations in one variable always have exactly one solution unless the variable terms cancel.
Source: ASVAB Math Knowledge — Linear Equations

Practice more questions

This question is from our ASVAB Practice Tests practice test. Take the full practice test to test your knowledge across all Algebra Basics and Equations and other topics.

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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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