Given the inequality |x - 56| < 116, which of the following values could represent x?

Given the inequality |x - 56| < 116, which of… | GMAT Sprint

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PS · Problem Solving

505-555

Inequalities

Given the inequality $|x - \frac{5}{6}| < \frac{11}{6}$ , which of the following values could represent x?

Answer Choices

Correct answer marked below

-4

-1

Correct

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Explanation

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Official Explanation

Official

To determine the possible values of x that meet the condition |x - 5/6| < 11/6, we can express this as -11/6 < (x - 5/6) < 11/6. By adding 5/6 to all parts of the inequality, we get -11/6 + 5/6 < x < 11/6 +…

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Comments

FabienAug 1, 2024

Can someone explain it other way?

NwokaApr 10, 2024

Good question

DevanganaSep 25

I keep getting confused by the 5/6, is that just part of the expression or does it change which choices work?

KritiOct 1

it shifts where x is centered but you still just test the choices, no need to overthink it

What this question tests

What it tests

Your ability to solve and combine linear inequalities and reason about ranges of values.

Common trap

Failing to flip the inequality sign when multiplying or dividing by a negative, or missing an inclusive/exclusive endpoint.

Given the inequality ∣x−56∣<116|x - \frac{5}{6}| < \frac{11}{6}∣x−65​∣<611​, which of the following values could represent x?