Question 7(Multiple Choice Worth 1 points) (01.05 LC) Which of the following is an equivalent form of the compound inequality -44gt -2x-8geqslant -48 -2x-8gt -44 and -2x-8geqslant -48 -2xgt -44 and -8geqslant -48 -2x-8lt -44 and -2x-8leqslant -48 -2x-8lt -44 and -2x-8geqslant -48

To solve the compound inequality $-44 > -2x - 8 \geq -48$, we need to break it down into two separate inequalities and solve each one.<br /><br />The first inequality is $-44 > -2x - 8$. To solve this inequality, we need to isolate the variable $x$.<br /><br />Step 1: Add 8 to both sides of the inequality:<br />$-44 + 8 > -2x$<br />$-36 > -2x$<br /><br />Step 2: Divide both sides of the inequality by -2 (and reverse the inequality sign):<br />$\frac{-36}{-2} < x$<br />$18 < x$<br /><br />The second inequality is $-2x - 8 \geq -48$. To solve this inequality, we need to isolate the variable $x$.<br /><br />Step 1: Add 8 to both sides of the inequality:<br />$-2x \geq -48 + 8$<br />$-2x \geq -40$<br /><br />Step 2: Divide both sides of the inequality by -2 (and reverse the inequality sign):<br />$x \leq \frac{-40}{-2}$<br />$x \leq 20$<br /><br />Therefore, the equivalent form of the compound inequality $-44 > -2x - 8 \geq -48$ is $-2x - 8 < -44$ and $-2x - 8 \geq -48$.<br /><br />So, the correct answer is:<br />$-2x-8\lt -44$ and $-2x-8\geqslant -48$