Question

solve for b and graph the solution. |5b + 50| - 1 ≤ 49 click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or two arrowheads to graph a line. to change endpoints from filled-in circles to empty circles, click on them.
-20 -15 -10 -5 0 5 10 15 20 25 30 35 40

Explanation:

Step1: Isolate the absolute value

Add 1 to both sides of the inequality:
$|5b + 50| - 1 + 1 \leq 49 + 1$
Simplify: $|5b + 50| \leq 50$

Step2: Solve the compound inequality

This splits into two inequalities:
$-50 \leq 5b + 50 \leq 50$

Step3: Subtract 50 from all parts

$-50 - 50 \leq 5b + 50 - 50 \leq 50 - 50$
Simplify: $-100 \leq 5b \leq 0$

Step4: Divide by 5

$\frac{-100}{5} \leq \frac{5b}{5} \leq \frac{0}{5}$
Simplify: $-20 \leq b \leq 0$

Answer:

The solution for \( b \) is \( -20 \leq b \leq 0 \). To graph this, plot a line segment with filled - in circles at \( -20 \) and \( 0 \) on the number line (since the inequality is "less than or equal to", the endpoints are included).