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 compound inequality on the left to the graph that represents its solution on the right. 8x < 24 and −8 ≤ 2x − 4 5x − 2 > 13 or −4x ≥ 8 −25 ≤ 9x + 2 < 20 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 $8x < 24$ and $-8 \leq 2x -4$

First, solve $8x < 24$:
$\frac{8x}{8} < \frac{24}{8}$
$x < 3$

Then solve $-8 \leq 2x -4$:
$-8 +4 \leq 2x$
$-4 \leq 2x$
$\frac{-4}{2} \leq x$
$x \geq -2$

Combined solution: $-2 \leq x < 3$

Step2: Solve $5x -2 >13$ or $-4x \geq8$

First, solve $5x -2 >13$:
$5x >13 +2$
$5x >15$
$\frac{5x}{5} > \frac{15}{5}$
$x >3$ (Note: correction from original, 13+2=15, 15/5=3)

Then solve $-4x \geq8$:
$\frac{-4x}{-4} \leq \frac{8}{-4}$ (reverse inequality when dividing by negative)
$x \leq -2$

Combined solution: $x \leq -2$ or $x >3$

Step3: Solve $-25 \leq9x +2 <20$

First, subtract 2 from all parts:
$-25 -2 \leq9x <20 -2$
$-27 \leq9x <18$

Divide all parts by 9:
$\frac{-27}{9} \leq x < \frac{18}{9}$
$-3 \leq x <2$

Answer:

1. $8x < 24$ and $-8 \leq 2x -4$ matches the graph with closed dot at $-2$, open dot at $3$, and shading between them (middle graph).
2. $5x - 2 > 13$ or $-4x \geq 8$ matches the graph with closed dot at $-2$ shading left, open dot at $3$ shading right (right graph).
3. $-25 \leq 9x + 2 < 20$ matches the graph with closed dot at $-3$, open dot at $2$, and shading between them (left graph).