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:

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:

Let's simplify the expression inside the parentheses:

So the equation becomes:

Now, distribute the 2:

Subtract 10 from both sides of the equation:

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

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