Question

what is the correct graph of the compound inequality 3x + 1 < -2 or 2x - 8 ≥ -18?
a. graph
-10 0 10
b. graph
-10 0 10
c. graph
-10 0 10
d. graph
-10 0 10
e. graph
-10 0 10
f. graph
-10 0 10
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set in interval notation is

b. the solution is the empty set.

Explanation:

Step1: Solve first inequality

$3x + 1 < -2$
Subtract 1 from both sides:
$3x < -2 - 1$
$3x < -3$
Divide by 3:
$x < -1$

Step2: Solve second inequality

$2x - 8 \geq -18$
Add 8 to both sides:
$2x \geq -18 + 8$
$2x \geq -10$
Divide by 2:
$x \geq -5$

Step3: Combine solution sets

The compound inequality uses "or", so we combine $x < -1$ and $x \geq -5$. This covers all real numbers, since every real number is either less than -1 or greater than/equal to -5 (which includes all values on the number line).

Answer:

C. <the number line spanning from -10 to 10 with the entire line shaded>
A. The solution set in interval notation is $(-\infty, \infty)$.