Find X in Rectangle with Perimeter 8: Sides (x-3) and (4+2x)

To find $x$, we'll use the concept of the rectangle's perimeter.

Step 1: Identify the given expressions for length and width.

• Length $L = 4 + 2x$
• Width $W = x - 3$
• Perimeter $P = 8$

Step 2: Use the formula for the perimeter of a rectangle: $P = 2(L + W)$.

Substitute the given expressions into the formula:

$8 = 2((4 + 2x) + (x - 3))$

Step 3: Simplify the equation within the parentheses:

$8 = 2(4 + 2x + x - 3)$ $8 = 2(1 + 3x)$

Step 4: Distribute the 2:

$8 = 2 \times 1 + 2 \times 3x$ $8 = 2 + 6x$

Step 5: Solve for $x$:

$8 - 2 = 6x$ $6 = 6x$ $x = 1$

Therefore, the value of $x$ is 1.