Solve: -7leqslant 2x+3lt 11 Give your answer as an interval. square

To solve the compound inequality $-7\leqslant 2x+3\lt 11$, we need to isolate the variable $x$.<br /><br />First, let's solve the left inequality $-7\leqslant 2x+3$.<br /><br />Subtract 3 from both sides:<br />$-7-3\leqslant 2x+3-3$<br />$-10\leqslant 2x$<br /><br />Divide both sides by 2:<br />$\frac{-10}{2}\leqslant \frac{2x}{2}$<br />$-5\leqslant x$<br /><br />Now, let's solve the right inequality $2x+3\lt 11$.<br /><br />Subtract 3 from both sides:<br />$2x+3-3\lt 11-3$<br />$2x\lt 8$<br /><br />Divide both sides by 2:<br />$\frac{2x}{2}\lt \frac{8}{2}$<br />$x\lt 4$<br /><br />Combining the two inequalities, we have $-5\leqslant x\lt 4$.<br /><br />Therefore, the solution to the compound inequality $-7\leqslant 2x+3\lt 11$ is the interval $[-5, 4)$.