Question

match each compound inequality on the left to the graph that represents its solution on the right.
-14 ≤ 6x + 4 < 16
-4x + 3 > -9 and -6x ≤ 12
-4x + 3 < -9 or 6x ≤ -12
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 cursor will change. need help? watch this video.

Explanation:

Step1: Solve the first inequality \(-14\leq6x + 4\lt16\)

Subtract \(4\) from all parts: \(-14-4\leq6x+4 - 4\lt16 - 4\), which simplifies to \(-18\leq6x\lt12\). Divide by \(6\): \(- 3\leq x\lt2\).

Step2: Solve the second inequality \(-4x + 3\gt-9\) and \(-6x\leq12\)

For \(-4x + 3\gt-9\), subtract \(3\): \(-4x\gt-12\), divide by \(-4\) (reverse inequality sign): \(x\lt3\). For \(-6x\leq12\), divide by \(-6\) (reverse inequality sign): \(x\geq - 2\). The solution is \(-2\leq x\lt3\).

Step3: Solve the third inequality \(-4x + 3\lt-9\) or \(6x\leq-12\)

For \(-4x + 3\lt-9\), subtract \(3\): \(-4x\lt-12\), divide by \(-4\) (reverse inequality sign): \(x\gt3\). For \(6x\leq-12\), divide by \(6\): \(x\leq - 2\). The solution is \(x\gt3\) or \(x\leq - 2\).

Answer:

\(-14\leq6x + 4\lt16\) matches the number - line with \(x\) from \(-3\) (closed circle) to \(2\) (open circle); \(-4x + 3\gt-9\) and \(-6x\leq12\) matches the number - line with \(x\) from \(-2\) (closed circle) to \(3\) (open circle); \(-4x + 3\lt-9\) or \(6x\leq-12\) matches the number - line with \(x\leq - 2\) (closed circle) and \(x\gt3\) (open circle).