Question

match the inequality on the left with the graph on the right.
4x - 2 > 6
4x - 2 ≥ 6
4x - 2 < 6
4x - 2 ≤ 6
(graphs: number lines with -8, -6, -4, -2, 0, 2, 4, 6, 8, some with filled or open circles and shaded regions)

Explanation:

Step1: Solve \(4x - 2>6\)

Add 2 to both sides: \(4x - 2 + 2>6 + 2\), so \(4x>8\). Divide by 4: \(x > 2\). The graph for \(x>2\) has an open circle at 2 and shading to the right. So \(4x - 2>6\) matches the second graph (open circle at 2, right shading).

Step2: Solve \(4x - 2\geq6\)

Add 2: \(4x\geq8\), divide by 4: \(x\geq2\). The graph has a closed circle at 2 and shading to the right. So \(4x - 2\geq6\) matches the fourth graph (closed circle at 2, right shading).

Step3: Solve \(4x - 2<6\)

Add 2: \(4x<8\), divide by 4: \(x < 2\). The graph has an open circle at 2 and shading to the left. So \(4x - 2<6\) matches the third graph (open circle at 2, left shading).

Step4: Solve \(4x - 2\leq6\)

Add 2: \(4x\leq8\), divide by 4: \(x\leq2\). The graph has a closed circle at 2 and shading to the left. So \(4x - 2\leq6\) matches the first graph (closed circle at 2, left shading).

Answer:

• \(4x - 2>6\) matches the second graph (open circle at 2, right - shaded number line).
• \(4x - 2\geq6\) matches the fourth graph (closed circle at 2, right - shaded number line).
• \(4x - 2<6\) matches the third graph (open circle at 2, left - shaded number line).
• \(4x - 2\leq6\) matches the first graph (closed circle at 2, left - shaded number line).