### Instruction: A trapezoid has one base equal to twice its height, $x$, and the other base is three times as long as the height. Write the expression for the area of the trapezoid as a common fraction in terms of the height $x$.### Response: We know that the area of a trapezoid is $\frac{1}{2}(b_1 + b_2)h$.
And we know that $b_1 = 2x$, $b_2 = 3x$, and $h = x$.
So the area is $\frac{1}{2}(2x + 3x)x$.
Then the area is $\frac{1}{2}(5x)x$.