Answer:
Absolute value inequality is |(2x + 12) - 12| < 2
Solution of the inequality is -1 < x < 1 (x = -1 or x = 1)
Step-by-step 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)
