Answer: the width of the frame is 3 inches.
Step-by-step explanation:
Let x represent the width of the frame.
If the length of the mirror is 10 inches, the length of the mirror and the frame would be (x + 10) inches
If the width of the mirror is 7 inches, the width of the mirror and the frame would be (x + 7) inches
The mirror and frame together cover an area of 130 inches squared. This means that
(x + 10)(x + 7) = 130
x² + 7x + 10x + 70 = 130
x² + 17x + 70 - 130 = 0
x² + 17x - 60 = 0
x² + 20x - 3x - 60 = 0
x(x + 20) - 3(x + 20) = 0
x - 3 = 0 or x + 20 = 0
x = 3 or x = - 20
Since the width cannot be negative, then x = 3
