Question

match each compound inequality on the left to the graph that represents its solution on the right.
-5x + 9 < -6 or -3x + 1 ≥ 7
-6x > -18 and 1 ≤ 2x + 5
-16 ≤ 6x + 2 < 14
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 the first compound inequality \(-5x + 9 < -6\) or \(-3x + 1\geq7\)

• Solve \(-5x+9 < -6\):

Subtract \(9\) from both sides: \(-5x<-6 - 9=-15\).
Divide both sides by \(- 5\) (and reverse the inequality sign): \(x > 3\).

• Solve \(-3x + 1\geq7\):

Subtract \(1\) from both sides: \(-3x\geq7 - 1 = 6\).
Divide both sides by \(-3\) (and reverse the inequality sign): \(x\leq - 2\).
The solution of the compound inequality \(-5x + 9 < -6\) or \(-3x + 1\geq7\) is \(x>3\) or \(x\leq - 2\).

Step2: Solve the second compound inequality \(-6x>-18\) and \(1\leq2x + 5\)

• Solve \(-6x>-18\):

Divide both sides by \(-6\) (and reverse the inequality sign): \(x < 3\).

• Solve \(1\leq2x+5\):

Subtract \(5\) from both sides: \(1-5\leq2x\), i.e., \(-4\leq2x\).
Divide both sides by \(2\): \(-2\leq x\).
The solution of the compound inequality \(-6x > - 18\) and \(1\leq2x + 5\) is \(-2\leq x<3\).

Step3: Solve the third compound inequality \(-16\leq6x + 2<14\)

• Subtract \(2\) from all parts: \(-16-2\leq6x+2 - 2<14 - 2\), i.e., \(-18\leq6x<12\).
• Divide all parts by \(6\): \(-3\leq x<2\).

Answer:

\(-5x + 9 < -6\) or \(-3x + 1\geq7\) matches the first graph (with \(x\leq - 2\) (blue - filled circle at \(-2\)) and \(x > 3\) (blue - open circle at \(3\))).
\(-6x > - 18\) and \(1\leq2x + 5\) matches the third graph (with \(-2\leq x<3\) (blue - filled circle at \(-2\) and blue - open circle at \(3\))).
\(-16\leq6x + 2<14\) matches the second graph (with \(-3\leq x<2\) (blue - filled circle at \(-3\) and blue - open circle at \(2\))).