Answer:
|24 - (2x - 6)| < 6
x > 12 or x < 18 (12 < x < 18)
Explanation:
Area of the triangle = ½*base*height = ½*8*6 = 4*6 = 24 unit²
Area of rectangle = length * width = (x - 3) * 2 = (2x - 6) unit²
Difference in their areas is given as less than 6. This can be represented as an absolute value of inequality as shown below:
|24 - (2x - 6)| < 6
Solve to find the solution of the inequality by splitting into two as follows:
24 - (2x - 6) < 6 OR 24 - (2x - 6) > -6
Solve for each
24 - 2x + 6 < 6
30 - 2x < 6
Subtract 30 from both sides
-2x < 6 - 30
-2x < -24
Divide both sides by -2. < will change to >, since we are dividing by a negative number.
x > 12
Or
24 - (2x - 6) > -6
24 - 2x + 6 > -6
30 - 2x > -6
Subtract 30 from both sides
-2x > -6 - 30
-2x > -36
Divide both sides by -2
x < 18
The solution of the inequality is x > 12 or x < 18
Or can be written as: 12 < x < 18