HELP ME PLEASE I CANT FIGURE THIS OUT

Question

Write an absolute value inequality that represents the situation. Then solve the inequality. 

The difference between the areas of the figures is less than 2.

 

The absolute value inequality is  . 

Question 2

The solution of the inequality is .

Answer 1

The area of the triangle is

A_t = ½bh = ½(4)(x + 6) = 2x + 12

The area of the rectangle is

A_r = 12

The difference between the areas of the figures is less than 2.

This means that

|A_t – A_r| < 2

which gives us

|2x + 12 – 12| < 2

and

|2x| < 2

So our final absolute inequality is

|x| < 1

Solving the absolute inequality gives

–1 < x < 1

Answer 2

Area of triangle = (1/2)(4)(x+6) = 2x + 12

Area of rectangle = (2)(6) = 12

So l (2x+12) - 12 l < 2

l 2x l < 2 So, -2 < 2x < 2.

-1 < x < 1