Question

ENGINEERING Tolerance is an allowance made for imperfections in a
manufactured object. The manufacturer of an oven specifies a temperature
tolerance of £15°F. This means that the temperature inside the oven will be within
15°F of the temperature to which it is set. Write and solve an absolute value
equation to find the maximum and minimum temperatures inside the oven when
the thermostat is set to 400°F.

Answer 1

Using an absolute value equation, it is found that:

• The maximum temperature is 415ºF.
• The minimum temperature is 385ºF.

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• The absolute value function measures the distance of a point to the origin.

• A less than compound inequality is represented by:

$|x| \leq a$

The solution is:

$-a \leq x \leq a$

In this problem:

• Temperature T set to 400ºF, with a tolerance of 15ºF, which means that the absolute value of the difference between the temperature T and 400ºF may be of at most 15ºF, that is:

$|T - 400| \leq 15$

Applying the solution:

$-15 \leq T - 400 \leq 15$

Then

$T - 400 \geq -15$

$T \geq 385$

$T - 400 \leq 15$

$T \leq 415$

• The maximum temperature is 415ºF.
• The minimum temperature is 385ºF.

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