Question

solve the compound inequality.
5(x - 4) < 10 or x + 5 > 9
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is
(type your answer in interval notation. simplify your answer. use integers or fractions for any numbers in the expression.)
b. the solution set is ∅.

Explanation:

Step1: Solve first inequality

First, expand and isolate $x$:
$5(x - 4) < 10$
$5x - 20 < 10$
$5x < 10 + 20$
$5x < 30$
$x < 6$

Step2: Solve second inequality

Isolate $x$ by subtracting 5:
$x + 5 > 9$
$x > 9 - 5$
$x > 4$

Step3: Combine solution sets

Since it's an "or" compound inequality, we combine all values that satisfy either inequality. All real numbers satisfy either $x < 6$ or $x > 4$.

Answer:

A. The solution set is $(-\infty, \infty)$