Question

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

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 (the first graph in the row of four graphs).
\(-5x + 6>16\) matches the graph with an open - circle at \(-2\) and shading to the left (the third graph in the row of four graphs).
\(10x + 2\leq - 18\) matches the graph with a closed - circle at \(-2\) and shading to the left (the second graph in the row of four graphs).
\(3x + 4>-2\) matches the graph with an open - circle at \(-2\) and shading to the right (the fourth graph in the row of four graphs).