Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. 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 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. clear

Explanation:

Step1: Solve the first compound - inequality

Solve \(-14\leq6x + 4<16\). First, subtract 4 from all parts: \(-14-4\leq6x+4 - 4<16 - 4\), which simplifies to \(-18\leq6x<12\). Then divide all parts by 6: \(\frac{-18}{6}\leq\frac{6x}{6}<\frac{12}{6}\), so \(- 3\leq x<2\).

Step2: Solve the second compound - inequality

For \(-4x + 3>-9\) and \(-6x\leq12\).

• Solve \(-4x + 3>-9\): Subtract 3 from both sides: \(-4x+3 - 3>-9 - 3\), so \(-4x>-12\). Divide both sides by - 4 and reverse the inequality sign: \(x < 3\).
• Solve \(-6x\leq12\): Divide both sides by - 6 and reverse the inequality sign: \(x\geq - 2\). The solution is \(-2\leq x<3\).

Step3: Solve the third compound - inequality

For \(-4x + 3<-9\) or \(6x\leq - 12\).

• Solve \(-4x + 3<-9\): Subtract 3 from both sides: \(-4x+3 - 3<-9 - 3\), so \(-4x<-12\). Divide both sides by - 4 and reverse the inequality sign: \(x>3\).
• Solve \(6x\leq - 12\): Divide both sides by 6: \(x\leq - 2\). The solution is \(x\leq - 2\) or \(x>3\).

Match the solutions to the graphs based on the endpoints and open/closed - circle rules (closed circle for \(\leq\) or \(\geq\), open circle for \(<\) or \(>\)).

Answer:

Match \(-14\leq6x + 4<16\) to the graph with a closed - circle at \(-3\) and an open - circle at 2.
Match \(-4x + 3>-9\) and \(-6x\leq12\) to the graph with a closed - circle at \(-2\) and an open - circle at 3.
Match \(-4x + 3<-9\) or \(6x\leq - 12\) to the graph with a closed - circle at \(-2\) and an open - circle on the right - hand side for \(x>3\) and including values \(x\leq - 2\).