Question

write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 140. select the correct answer below and fill in the answer box to complete your choice. a. x≥ b. x≤ c. x> d. x<

Explanation:

Step1: Recall the formula for the perimeter of a rectangle

The perimeter \(P\) of a rectangle is given by \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width. Here, \(l=x + 4\) and \(w=x\). So, \(P=2((x + 4)+x)\).

Step2: Simplify the perimeter formula

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Step3: Set up the inequality

We want the perimeter to be less than \(140\), so \(4x + 8<140\).

Step4: Solve the inequality for \(x\)

Subtract \(8\) from both sides: \(4x+8 - 8<140 - 8\), which gives \(4x<132\).
Divide both sides by \(4\): \(\frac{4x}{4}<\frac{132}{4}\), so \(x < 33\).

Answer:

D. \(x<33\)