Question

solve for x.
-18x + 21 > -15 or 20x - 13 ≥ 27
choose 1 answer:
a ( x < -2 ) or ( x ge 2 )
b ( x = -2 )
c ( x ge 2 )
d there are no solutions
e all values of x are solutions

Explanation:

Step1: Isolate x in first inequality

Subtract 21 from both sides:
$-18x > -15 - 21$
$-18x > -36$
Divide by -18 (reverse inequality):
$x < \frac{-36}{-18}$
$x < 2$

Step2: Isolate x in second inequality

Add 13 to both sides:
$20x \geq 27 + 13$
$20x \geq 40$
Divide by 20:
$x \geq \frac{40}{20}$
$x \geq 2$

Step3: Combine "OR" solutions

The compound inequality requires either $x < 2$ or $x \geq 2$, which covers all real numbers.

Answer:

E. All values of $x$ are solutions