Question

solve the following compound inequality. -22 < 4x + 6 ≤ 50 ? < x ≤

Explanation:

Step1: Subtract 6 from all parts

To isolate the term with \(x\), we subtract 6 from each part of the compound inequality. So we have \(-22 - 6<4x + 6-6\leq50 - 6\), which simplifies to \(-28 < 4x\leq44\).

Step2: Divide all parts by 4

To solve for \(x\), we divide each part of the inequality by 4. So \(\frac{-28}{4}<\frac{4x}{4}\leq\frac{44}{4}\), which simplifies to \(-7 < x\leq11\).

Answer:

\(-7 < x\leq11\) (So the first box is \(-7\) and the second box is \(11\))