Question

M

A "normal" temperature for a certain animal is 86.6°F. If a temperature x that differs from the normal by at least 2.5°F is considered unhealthy, write the condition for an
unhealthy temperature x as an inequality involving an absolute value, and solve for x

Write the condition for an unhealthy temperature x as an inequality involving an absolute value.
(Use integers or decimals for any numbers in the inequality.)

Answer 1

Explanation:

The condition for an unhealthy temperature x can be written as:

| x - 86.6°F | ≥ 2.5°F

This inequality states that the absolute value of the difference between x and 86.6°F must be greater than or equal to 2.5°F for the temperature to be considered unhealthy.

To solve for x, we can write two separate inequalities:

x - 86.6°F ≥ 2.5°F (when x - 86.6°F is positive)

or

x - 86.6°F ≤ -2.5°F (when x - 86.6°F is negative)

Solving the first inequality:

x ≥ 2.5°F + 86.6°F

x ≥ 89.1°F

Solving the second inequality:

x ≤ -2.5°F + 86.6°F

x ≤ 84.1°F

Therefore, an unhealthy temperature x would be any value less than or equal to 84.1°F or greater than or equal to 89.1°F.