Solve and graph the compound inequality. \( -7

Ask by Lawson Kelley. in the United States

Feb 18,2025

To solve the compound inequality \( -7 < x + 1 < 5 \), we'll break it into two separate inequalities: 1. For the left side: \[ -7 < x + 1 \] Subtract 1 from both sides: \[ -8 < x \quad \text{or} \quad x > -8 \] 2. For the right side: \[ x + 1 < 5 \] Subtract 1 from both sides: \[ x < 4 \] Combining these two results, we have: \[ -8 < x < 4 \] To graph this compound inequality on a number line, we would: - Draw an open circle on -8 to indicate that -8 is not included in the solution. - Draw another open circle on 4 for the same reason. - Shade the region between -8 and 4. This tells us that x can take any value greater than -8 and less than 4!