Question

write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 128.

select the correct answer below and fill in the answer box to complete your choice.

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Explanation:

Step1: Write the formula for the perimeter of a rectangle

The perimeter \(P\) of a rectangle is given by \(P = 2(l + w)\), where \(l=x + 4\) and \(w=x\). So \(P=2((x + 4)+x)=2(2x + 4)=4x+8\)

Step2: Set up the inequality

We want the perimeter to be less than \(128\), so \(4x + 8<128\)

Step3: Solve the inequality for \(x\)

Subtract \(8\) from both sides: \(4x+8 - 8<128 - 8\), which gives \(4x<120\). Then divide both sides by \(4\): \(\frac{4x}{4}<\frac{120}{4}\), so \(x < 30\)

Answer:

A. \(x<30\)