Suppose you measured the diameter of a tree trunk to be 5 cm. The actual diameter can vary by at most 0.4 cm, due to the error in measuring a non-flat surface. Write an absolute value inequality for the range of acceptable diameters and solve the inequality.

Joe mama

4.6cm <=diameter<=5.4cm

To write an absolute value inequality for the range of acceptable diameters, we need to account for the maximum allowable error of 0.4 cm. Since the actual diameter can vary by at most 0.4 cm from the measured diameter of 5 cm, we can set up the following inequality:

|actual diameter - measured diameter| ≤ maximum allowable error

Replacing the variables with their respective values, we get:

|actual diameter - 5| ≤ 0.4

Now, we can solve this inequality by breaking it down into two separate inequalities:

1. actual diameter - 5 ≤ 0.4
2. actual diameter - 5 ≥ -0.4

1. Solving the first inequality:

actual diameter - 5 ≤ 0.4
Adding 5 to both sides:
actual diameter ≤ 0.4 + 5
actual diameter ≤ 5.4

2. Solving the second inequality:

actual diameter - 5 ≥ -0.4
Adding 5 to both sides:
actual diameter ≥ -0.4 + 5
actual diameter ≥ 4.6

Therefore, the absolute value inequality for the range of acceptable diameters is:

4.6 ≤ actual diameter ≤ 5.4