Question

The difference between the areas of the figures is less than 8.

An absolute value inequality that represents this situation is _.
The solution of the inequality is_.

Answer 1

• | 4x - 8 - 6 | < 8
• 1.5 < x < 5.5

Explanation:

Area of the figures

Rectangle:

• 4(x - 2) = 4x - 8

Triangle:

• 1/2*3*4 = 6

The difference between the areas, inequality:

• | 4x - 8 - 6 | < 8

Solution

• | 4x - 14 |< 8
• 1. 4x - 14 < 8 ⇒ 4x < 22 ⇒ x < 22/4 ⇒ x < 5.5
• 2. 4x - 14 > -8 ⇒ 4x > 6 ⇒ x > 6/4 ⇒ x > 1.5
• x = (1.5, 5.5)