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The solution set of the linear inequation ∣4x−3∣≤34|4x - 3| \leq \frac{3}{4} is:

Solution

✅ Correct Option: 3

The inequality ∣4x−3∣≤34|4x - 3| \leq \frac{3}{4} can be rewritten using the property that ∣A∣≤B|A| \leq B means −B≤A≤B-B \leq A \leq B.

−34≤4x−3≤34-\frac{3}{4} \leq 4x - 3 \leq \frac{3}{4}


Adding 33 to all parts:

−34+3≤4x≤34+3-\frac{3}{4} + 3 \leq 4x \leq \frac{3}{4} + 3

Converting 3=1243 = \frac{12}{4}:

−34+124≤4x≤34+124-\frac{3}{4} + \frac{12}{4} \leq 4x \leq \frac{3}{4} + \frac{12}{4}

94≤4x≤154\frac{9}{4} \leq 4x \leq \frac{15}{4}


Dividing all parts by 44:

94⋅14≤x≤154⋅14\frac{9}{4} \cdot \frac{1}{4} \leq x \leq \frac{15}{4} \cdot \frac{1}{4}

916≤x≤1516\frac{9}{16} \leq x \leq \frac{15}{16}


Since the inequality uses ≤\leq, the endpoints are included in the solution set.

Therefore, x∈[916,1516]x \in \left[\frac{9}{16}, \frac{15}{16}\right]

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