Question

solve the compound inequality. give the solution set in both interval and graph forms.
$x + 1 \geq 8$ and $x - 5 \leq 10$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
\\(\bigcirc\\) a. the solution set is \\(
\\).
(type your answer in interval notation.)
\\(\bigcirc\\) b. the solution set is \\(\varnothing\\).

Explanation:

Step1: Solve first inequality

$x + 1 \geq 8$
Subtract 1 from both sides:
$x \geq 8 - 1$
$x \geq 7$

Step2: Solve second inequality

$x - 5 \leq 10$
Add 5 to both sides:
$x \leq 10 + 5$
$x \leq 15$

Step3: Find intersection of solutions

Combine $x \geq 7$ and $x \leq 15$, so the solution is $7 \leq x \leq 15$, which in interval notation is $[7, 15]$.

Graph Description:

A number line with a closed dot at 7 and a closed dot at 15, with the segment between the two dots shaded.

Answer:

A. The solution set is $[7, 15]$