Question

match each compound inequality on the left to the graph that represents its solution on the right.
4x + 3 > 15 or -6x ≥ 12
-8x > -24 and -10 ≤ 2x - 6
-29 ≤ 9x - 2 < 16
clear
click and hold an item in one column, then drag it to the matching item in the other column. be sure your cursor is over the target before releasing. the target will highlight or the cursor will change. need help? watch this video.

Explanation:

Step1: Solve \(4x + 3>15\)

Subtract 3 from both sides: \(4x>15 - 3\), so \(4x>12\). Divide by 4: \(x > 3\).
Solve \(-6x\geq12\). Divide by \(-6\) (reverse inequality sign): \(x\leq - 2\). The solution is \(x>3\) or \(x\leq - 2\).

Step2: Solve \(-8x>-24\)

Divide by \(-8\) (reverse inequality sign): \(x < 3\).
Solve \(-10\leq2x - 6\). Add 6 to both sides: \(-4\leq2x\). Divide by 2: \(-2\leq x\). The solution is \(-2\leq x<3\).

Step3: Solve \(-29\leq9x - 2<16\)

Add 2 to all parts: \(-27\leq9x<18\). Divide by 9: \(-3\leq x < 2\).

Answer:

\(4x + 3>15\) or \(-6x\geq12\) matches the graph with a closed - circle at \(-2\) and an open - circle at \(3\).
\(-8x > - 24\) and \(-10\leq2x - 6\) matches the graph with a closed - circle at \(-2\) and an open - circle at \(3\).
\(-29\leq9x - 2<16\) matches the graph with a closed - circle at \(-3\) and an open - circle at \(2\).