Question

8
$ac = 18x + 5$
$bd = 15x + 11$
$x = \\_\\_\\_\\_$

Explanation:

Step1: Recognize equal diagonals property

In an isosceles trapezoid (since $BC \parallel AD$ and $AB=CD$), diagonals are equal, so $AC=BD$.

Step2: Set up equation

Substitute given expressions:
$18x + 5 = 15x + 11$

Step3: Solve for $x$

Subtract $15x$ from both sides:
$3x + 5 = 11$
Subtract 5 from both sides:
$3x = 6$
Divide by 3:
$x = \frac{6}{3} = 2$

Answer:

$x=2$