Question

solve each two - step inequality and match the answer to the graph
12 - 4x ≤ 20
-5x + 6 > 16
10x + 2 ≤ -18
3x + 4 > -2
choice
bj

Explanation:

Step1: Solve \(12 - 4x\leq20\)

Subtract \(12\) from both sides: \(12-4x - 12\leq20 - 12\), so \(-4x\leq8\). Divide both sides by \(- 4\) (reverse the inequality sign): \(x\geq - 2\).

Step2: Solve \(-5x + 6>16\)

Subtract \(6\) from both sides: \(-5x+6 - 6>16 - 6\), so \(-5x>10\). Divide both sides by \(-5\) (reverse the inequality sign): \(x<-2\).

Step3: Solve \(10x + 2\leq - 18\)

Subtract \(2\) from both sides: \(10x+2 - 2\leq - 18 - 2\), so \(10x\leq - 20\). Divide both sides by \(10\): \(x\leq - 2\).

Step4: Solve \(3x + 4>-2\)

Subtract \(4\) from both sides: \(3x + 4-4>-2 - 4\), so \(3x>-6\). Divide both sides by \(3\): \(x>-2\).

Answer:

• \(12 - 4x\leq20\) matches the graph with a closed - circle at \(-2\) and shading to the right.
• \(-5x + 6>16\) matches the graph with an open - circle at \(-2\) and shading to the left.
• \(10x + 2\leq - 18\) matches the graph with a closed - circle at \(-2\) and shading to the left.
• \(3x + 4>-2\) matches the graph with an open - circle at \(-2\) and shading to the right.