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Inequalities Involving Modulus Function

Solve the abs...

Question

Solve the absolute value of inequation $∣ ∣ ∣ \frac{2 x - 1}{3} ∣ ∣ ∣ \leq 5$ .

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Solution

Inequality condition

$∣ ∣ ∣ \frac{2 x - 1}{3} ∣ ∣ ∣ \leq 5 \Rightarrow | 2 x - 1 | \leq 15 \Rightarrow - 15 \leq 2 x - 1 \leq + 15 \Rightarrow - 14 \leq 2 x \leq + 16 \Rightarrow - 7 \leq x \leq + 8$

$∴ x = (- 7, 8)$ is the solution set of the given inequality.

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Inequalities Involving Modulus Function

Standard XII Mathematics

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