Question

1. use the rectangle diagram at the right.

part a
write and solve an inequality to find the values of x for which the
perimeter of the rectangle is less than 12.24.
part b
based on your answer to part a, are there any values that can be eliminated
from the solution set? explain.

Explanation:

Step1: Write the perimeter formula

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

Step2: Set up the inequality

We know that \( P<12.24 \). Substituting the perimeter formula, we get \( 2x + 8<12.24 \).

Step3: Solve the inequality

Subtract 8 from both sides: \( 2x+8 - 8<12.24 - 8 \), which simplifies to \( 2x<4.24 \). Then divide both sides by 2: \( x<\frac{4.24}{2}=2.12 \).

Step4: Consider the geometric constraint

Since \( x \) represents the length of a side of a rectangle, \( x>0 \).

Answer:

For Part A: The inequality is \( 2x + 8<12.24 \) and the solution is \( 0For Part B: Since \( x>0 \) (a side - length of a rectangle cannot be non - positive), values of \( x\leq0 \) can be eliminated from the solution set.