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Question

Mathematics Question on linear inequalities

If ∣3x−5∣≤2| 3x -5| \le 2, then

A

1≤x≤931 \le x \le \frac{9}{3}

B

−1≤x≤73 - 1 \le x \le \frac{7}{3}

C

−1≤x≤93 - 1 \le x \le \frac{9}{3}

D

1≤x≤731 \le x \le \frac{7}{3}

Answer

1≤x≤731 \le x \le \frac{7}{3}

Explanation

Solution

∣3x−5∣≤2\left|3x-5\right| \le2
⇒ −2≤3x−5≤2\Rightarrow\, -2 \le3x-5\le2
⇒ 3≤3x≤7\Rightarrow\, 3\le3x\le7
⇒ 1≤x≤73\Rightarrow\, 1\le x \le\frac{7}{3}