Question

solve for b and graph the solution.
36 ≥ 4|b - 20| - 4
click two endpoints to graph a line segment, an endpoint and an arrowhead to ray, or two arrowheads to graph a line. to change endpoints from filled - in circles to circles, click on them.
-20 -15 -10 -5 0 5 10 15 20 25 30 35
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Explanation:

Step1: Isolate the absolute value expression

First, we add 4 to both sides of the inequality \(36 \geq 4|b - 20| - 4\) to isolate the absolute value term.
\(36 + 4 \geq 4|b - 20|\)
\(40 \geq 4|b - 20|\)

Step2: Divide both sides by 4

Next, we divide both sides of the inequality by 4 to solve for the absolute value expression.
\(\frac{40}{4} \geq |b - 20|\)
\(10 \geq |b - 20|\)

Step3: Rewrite the absolute value inequality

The absolute value inequality \(|b - 20| \leq 10\) (since \(10 \geq |b - 20|\) is equivalent to \(|b - 20| \leq 10\)) can be rewritten as a compound inequality:
\(-10 \leq b - 20 \leq 10\)

Step4: Solve for b

We add 20 to all parts of the compound inequality to solve for \(b\).
\(-10 + 20 \leq b - 20 + 20 \leq 10 + 20\)
\(10 \leq b \leq 30\)

Answer:

The solution for \(b\) is \(10 \leq b \leq 30\). To graph this, we plot a line segment with endpoints at \(b = 10\) (filled - in circle) and \(b = 30\) (filled - in circle) on the number line.