Question

unit: solving equations and inequalities progress: 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 inequality on the left with its correct solution on the right. some answer choices on the right will be used more than once. 4x + 1 > 9 and -6x - 2 > 10 |3x| < 6 |x + 2| + 5 < 4 |2x + 4| > 2 -2 < x < 2 x > -1 or x < -3 no solution 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 compound inequality

First, solve $4x + 1 > 9$:
$4x > 9 - 1$
$4x > 8$
$x > 2$

Then solve $-6x - 2 > 10$:
$-6x > 10 + 2$
$-6x > 12$
$x < -2$
There is no overlap between $x > 2$ and $x < -2$, so this has no solution.

Step2: Solve $|3x| < 6$

Apply absolute value rule: $-6 < 3x < 6$
Divide all parts by 3:
$\frac{-6}{3} < x < \frac{6}{3}$
$-2 < x < 2$

Step3: Solve $|x+2| + 5 < 4$

Isolate absolute value:
$|x+2| < 4 - 5$
$|x+2| < -1$
Absolute value cannot be negative, so no solution.

Step4: Solve $|2x+4| > 2$

Apply absolute value rule: $2x+4 > 2$ or $2x+4 < -2$
First case: $2x > 2 - 4$ → $2x > -2$ → $x > -1$
Second case: $2x < -2 - 4$ → $2x < -6$ → $x < -3$
Result: $x > -1$ or $x < -3$

Answer:

• $4x + 1 > 9$ and $-6x - 2 > 10$ : no solution
• $|3x| < 6$ : $-2 < x < 2$
• $|x + 2| + 5 < 4$ : no solution
• $|2x + 4| > 2$ : $x > -1$ or $x < -3$