Final Answer:
The possible values of x when the area should be no more than 72 in² is all numbers less than or equal to 6 inches.
Step-by-step explanation:
To find the possible values of x, we'll use the formula for the area of a triangle, which is:
Area = 1/2 base*height
Given that the base of the triangle is 12 inches and the height is expressed as (x + 6) inches, we can represent the area of the triangle in terms of x as follows:
Area = 1/2 (12)*(x + 6)
According to the condition provided, the area of the triangle is no more than 72 square inches, so we can write the inequality:
1/2 (12)*(x + 6) ≤ 72
Let's solve this inequality for x:
(6)*(x + 6) ≤ 72
6x + 36 ≤ 72
Now, subtract 36 from both sides to isolate the term with x:
6x ≤ 72 - 36
6x ≤ 36
Finally, divide both sides of the inequality by 6 to solve for x:
x ≤ 36/6
x ≤ 6
Therefore, the possible values of x are such that x is less than or equal to 6 inches. In interval notation, the solution set for x would be written as:
x = (-∞, 6]
This means that x can be any real number up to and including 6 inches.