Algebra practice question

Answer: A. 1 < x ≤ 10

Multiply all three parts by 3: −6 ≤ 4 − x < 3. Subtract 4: −10 ≤ −x < −1. Multiply by −1 and reverse both signs: 10 ≥ x > 1, that is, 1 < x ≤ 10.

Why the other answers are wrong

B. −10 ≤ x < −1

−10 ≤ x < −1 is the result before multiplying by −1. That last step flips the signs AND the direction of the inequalities.

C. 1 ≤ x < 10

The endpoints belong to the wrong sides. Check x = 1: (4 − 1)/3 = 1, which is NOT less than 1. Check x = 10: (4 − 10)/3 = −2, which IS allowed.

D. −1 < x ≤ 10

x = 0 gives 4/3, which is not less than 1, so −1 < x ≤ 10 includes values that fail.

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