5geqslant vert 3x-1vert geqslant 2

To solve the inequality $5\geqslant \vert 3x-1\vert \geqslant 2$, we need to consider two cases:<br /><br />Case 1: $3x-1\geqslant 0$<br />In this case, the inequality becomes $5\geqslant 3x-1\geqslant 2$. Solving this inequality, we get $\frac{7}{3}\leqslant x\leqslant \frac{6}{3}$.<br /><br />Case 2: $3x-1<0$<br />In this case, the inequality becomes $5\geqslant -(3x-1)\geqslant 2$. Solving this inequality, we get $-\frac{6}{3}\leqslant x\leqslant -\frac{7}{3}$.<br /><br />Therefore, the solution to the inequality $5\geqslant \vert 3x-1\vert \geqslant 2$ is $-\frac{6}{3}\leqslant x\leqslant -\frac{7}{3}$ or $\frac{7}{3}\leqslant x\leqslant \frac{6}{3}$.