Solve for X: Rectangle AEFD with Perimeter 30 and Expression 2x+3

To solve the problem, we'll begin by setting up the equation for the perimeter of rectangle $AEFD$:

The perimeter $P$ of a rectangle is given by the formula:

$P = 2 \times (\text{length} + \text{width})$

We're told that the perimeter of rectangle $AEFD$ is 30. The length is $2x + 3$ and the width is $2 - x$. Thus, the perimeter equation is:

$2 \times ((2x + 3) + (2 - x)) = 30$

Let's simplify the expression inside the parentheses:

$= 2 \times ((2x + 3) + 2 - x)$ $= 2 \times (x + 5)$

So the equation becomes:

$2 \times (x + 5) = 30$

Now, distribute the 2:

$2x + 10 = 30$

Subtract 10 from both sides of the equation:

$2x = 20$

Divide both sides by 2 to solve for $x$:

$x = 10 \div 2$ $x = 2$

Therefore, the value of $x$ that satisfies the given perimeter is $x = 2$.