Question

For tropical fish, aquarium water should be set to 76° F with an allowance of 4°.

a. Explain how to write an absolute value equation to represent this situation.

b. Explain the steps to solve the absolute value equation. What do the solutions represent?

Answer 1

Using absolute value, it is found that:

• The absolute value equation that models the situation is: $|T - 76| = 4$

• The two solutions, $T = 72$ and $T = 80$, mean that the temperature of the aquarium water must be between these two values.

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• The absolute value function is defined by:

$|x| = x, x \geq 0$

$|x| = -x, x < 0$

• It measures the distance of a point x to the origin.

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Item a:

The temperature should be set to 76ºF with an allowance of 4ºF, thus, the absolute value of the difference between the temperature T and 76 should be 4, that is:

$|T - 76| = 4$

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Item b:

• Here, it is needed to solve the equation.

There are two solutions:

$T - 76 = 4$

$T = 80$

Or also:

$T - 76 = -4$

$T = 72$

• The two solutions, $T = 72$ and $T = 80$, mean that the temperature of the aquarium water must be between these two values.

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