Question

solve and graph the following inequality: ( 8 leq 4x + 5 leq 9 )

Explanation:

Step1: Subtract 5 from all parts

Subtract 5 from \(8\leq4x + 5\leq9\).

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Step2: Divide by 4

Divide each part by 4.

$$
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For the graph:

• On a number - line, place a closed circle (because the inequality includes equality, \(\leq\)) at \(x = \frac{3}{4}\) (or \(0.75\)) and at \(x = 1\).
• Then draw a line segment connecting these two closed circles.

Answer:

The solution of the inequality is \(\frac{3}{4}\leq x\leq1\). On the number - line, there are closed circles at \(x=\frac{3}{4}\) and \(x = 1\) with a line segment between them.