## Precalculus (6th Edition) Blitzer

$[\displaystyle \frac{3}{2},\frac{11}{2})$
The idea is to isolate $x$ in the middle. Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbols remain). Multiplying/dividing with a negative number inverts the order (the inequality symbols changes). --- $3\leq 4x-3 \lt 19 \qquad$ ... add $3$ to all $6\leq 4x \lt 22 \qquad$ ... divide with $4$ $\displaystyle \frac{6}{4}\leq x \lt \frac{22}{4}$ $\displaystyle \frac{3}{2}\leq x \lt \frac{11}{2}$ ... left border included, right border excluded The solution set is $[\displaystyle \frac{3}{2},\frac{11}{2})$ .