Question

use the rectangle diagram.
a. write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 120.
b. based on your answer to part a, are there any values that can be eliminated from the solution set? explain.
c. ( 2x + 2(x + 4) lt 120 )
d. ( x + x + 4 gt 120 )
solve the inequality. select the correct answer and fill in the answer box to complete your choice.
a. ( x geq )
b. ( x lt )

Explanation:

Step1: Expand the inequality

$$2x + 2(x + 4)<120$$
$$2x+2x + 8<120$$

Step2: Combine like terms

$$4x+8<120$$

Step3: Subtract 8 from both sides

$$4x+8 - 8<120 - 8$$
$$4x<112$$

Step4: Divide both sides by 4

$$\frac{4x}{4}<\frac{112}{4}$$
$$x < 28$$

For part b, since \(x\) represents a side - length of a rectangle, \(x>0\). So values of \(x\) such that \(x\leq0\) can be eliminated from the solution set \(x < 28\) because the length of a side of a rectangle cannot be non - positive.

Answer:

a. \(x<28\)
b. Yes. Values of \(x\) such that \(x\leq0\) can be eliminated. Because \(x\) represents the length of a side of a rectangle, and length cannot be non - positive.