The length of a rectangle is seven less than twice the length of its width. If the area of the rectangle is 15 square meters, then find the value of x.
Let the width of the rectangle be x meters.
Then the length of the rectangle is 2x - 7 meters.
The area of the rectangle is given by:
Area = length x width
15 = (2x - 7) x
Expanding the right side:
15 = 2x^2 - 7x
Rearranging the equation:
2x^2 - 7x - 15 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula. After solving, we get:
x = 3 or x = -2.5
Since the width of the rectangle cannot be negative, the value of x is 3.