Questions: Match each compound inequality on the left to the graph that represents its solution on the right. -5x + 9 < -6 or -3x + 1 ≥ 7 -6x > -18 and 1 ≤ 2x + 5 -16 ≤ 6x + 2 < 14

Transcript text: Match each compound inequality on the left to the graph that represents its solution on the right. \[ \begin{array}{l} -5 x+9<-6 \text { or }-3 x+1 \geq 7 \\ -6 x>-18 \text { and } 1 \leq 2 x+5 \\ -16 \leq 6 x+2<14 \end{array} \]

Solution

Solution Steps

Step 1: Identify the first compound inequality

The first compound inequality given is: \[ -5x + 9 \leq -6 \quad \text{or} \quad -3x + 1 \geq 7 \]

Step 2: Solve the first part of the compound inequality

Solve \(-5x + 9 \leq -6\): \[ -5x + 9 \leq -6 \] Subtract 9 from both sides: \[ -5x \leq -15 \] Divide by -5 (remember to reverse the inequality sign): \[ x \geq 3 \]

Step 3: Solve the second part of the compound inequality

Solve \(-3x + 1 \geq 7\): \[ -3x + 1 \geq 7 \] Subtract 1 from both sides: \[ -3x \geq 6 \] Divide by -3 (remember to reverse the inequality sign): \[ x \leq -2 \]

Step 4: Combine the solutions

The solution to the compound inequality \(-5x + 9 \leq -6 \quad \text{or} \quad -3x + 1 \geq 7\) is: \[ x \geq 3 \quad \text{or} \quad x \leq -2 \]

Step 5: Match the solution to the graph

Identify the graph that represents \(x \geq 3\) or \(x \leq -2\). The correct graph will have shading to the right of 3 and to the left of -2.