Solve the following inequality: left|frac{3x- | vedclass

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(A) Given the inequality: $\left|\frac{3x-4}{2}\right| \leq \frac{5}{12}$ This is equivalent to: $-\frac{5}{12} \leq \frac{3x-4}{2} \leq \frac{5}{12}$

Vedclass · Accepted Answer

$[\frac{19}{18}, \frac{29}{18}]$

Vedclass · Answer

(A) Given the inequality: $\left|\frac{3x-4}{2}\right| \leq \frac{5}{12}$ This is equivalent to: $-\frac{5}{12} \leq \frac{3x-4}{2} \leq \frac{5}{12}$ Multiply the entire inequality by $2$: $-\frac{5}{6} \leq 3x-4 \leq \frac{5}{6}$ Add $4$ to all parts: $4 - \frac{5}{6} \leq 3x \leq 4 + \frac{5}{6}$ $\frac{24-5}{6} \leq 3x \leq \frac{24+5}{6}$ $\frac{19}{6} \leq 3x \leq \frac{29}{6}$ Divide by $3$: $\frac{19}{18} \leq x \leq \frac{29}{18}$ Thus,the solution set is $[\frac{19}{18}, \frac{29}{18}]$.

Solve the following inequality: $\left|\frac{3x-4}{2}\right| \leq \frac{5}{12}$

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