Question

write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 104.$x + 4$$x$select the correct answer below and fill in the answer box to complete your choice○ a. $x <$○ b. $x >$○ c. $x \leq$○ d. $x \geq$help me solve this view an example get more help .

Explanation:

Step1: Recall rectangle perimeter formula

The perimeter $P$ of a rectangle is $P=2(l+w)$, where $l=x+4$ and $w=x$.

Step2: Set up inequality for perimeter

We need $P < 104$, so substitute the sides:
$2[(x+4)+x] < 104$

Step3: Simplify inside the parentheses

Combine like terms:
$2(2x+4) < 104$

Step4: Distribute the 2

Multiply through the parentheses:
$4x+8 < 104$

Step5: Subtract 8 from both sides

Isolate the term with $x$:
$4x < 104-8$
$4x < 96$

Step6: Divide by 4 to solve for x

Solve for $x$:
$x < \frac{96}{4}$
$x < 24$

Answer:

A. $x < 24$