Question

Please helppppppppppop

Write an absolute value inequality that represents the situation. Then solve the inequality the difference between the areas of the figure is less than 2.



The absolute value inequality is________<2


The solution of inequality is_______.

Answer 1

Absolute value inequality is |(2x + 12) - 12| < 2

Solution of the inequality is -1 < x < 1 (x = -1 or x = 1)

Explanation:

Area of triangle = ½*base*height = ½*4*(x + 6) = 2(x + 6) = 2x + 12

Area of rectangle = length * width = 6*2 = 12

Given that the difference their areas is less than two, therefore, an absolute value inequality can be written as follows:

|(2x + 12) - 12| < 2

Find the solution by splitting the inequality into two:

(2x + 12) - 12 < 2 OR (2x + 12) - 12 > -2

Solve each

2x + 12 - 12 < 2

2x < 2

2x/2 < 2/2

x < 1

OR

2x + 12 - 12 > -2

2x > -2

2x/2 > -2/2

x > -1

Solution would be -1 < x < 1 (x = -1 or x = 1)