Question

match each equation or inequality to its corresponding number line
answer choices
a
b
c
d
e
$-|2x - 3| = -9$
$-8x + 2 = 18$ or $4x - 5 = 14$
$-12 \leq 6x \leq 4$
$9x + 3 < -15$ or $\frac{3}{2}x - 5 > 1$
$|5x - 6| < 14$

d

b

c

e

a

Explanation:

Step1: Solve $-|2x-3|=-9$

First, isolate the absolute value:
$|2x-3|=9$
Split into two cases:
$2x-3=9$ or $2x-3=-9$
For $2x-3=9$: $2x=12$ → $x=6$
For $2x-3=-9$: $2x=-6$ → $x=-3$
This matches number line C (points at -3 and 6).

Step2: Solve $-8x+2=18$ or $4x-5=14$

Solve first equation:
$-8x=16$ → $x=-2$
Solve second equation:
$4x=19$ → $x=\frac{19}{4}=4.75$
This matches number line A (points at -2 and ~4.75).

Step3: Solve $-12\leq6x\leq4$

Divide all parts by 6:
$\frac{-12}{6}\leq x\leq\frac{4}{6}$ → $-2\leq x\leq\frac{2}{3}\approx0.67$
This matches number line D (segment from -2 to ~0.67).

Step4: Solve $9x+3<-15$ or $\frac{3}{2}x-5>1$

Solve first inequality:
$9x<-18$ → $x<-2$
Solve second inequality:
$\frac{3}{2}x>6$ → $x>4$
This matches number line B (rays left of -2, right of 4).

Step5: Solve $|5x-6|<14$

Rewrite as compound inequality:
$-14<5x-6<14$
Add 6 to all parts:
$-8<5x<20$
Divide by 5:
$\frac{-8}{5}This matches number line E (segment from -1.6 to 4).

Answer:

$-|2x-3|=-9$ → C
$-8x+2=18$ or $4x-5=14$ → A
$-12\leq6x\leq4$ → D
$9x+3<-15$ or $\frac{3}{2}x-5>1$ → B
$|5x-6|<14$ → E