Question

The thermometer in a freezer is set to -2 degrees Fahrenheit. This temperature varies by up to 3 degrees throughout the day. Write and solve an absolute value inequality that represents the range of temperatures(in degrees Fahrenheit) of the freezer throughout the day. Use t for your variable.​

Answer 1

Answer:

The temperature can vary from -5°F to 1°F on the freezer

Step-by-step explanation:

Inequalities

Let t be the temperature in degrees Fahrenheit. It was originally set to -2°F. The variation of the temperature throughout the day can be calculated as:

variation=t-(-2)=t+2

We know the temperature can vary by up to 3°F. Since the variation can be positive or negative, we must take the absolute value to comply with the restriction, that is:

$|t+2|\le 3$

That is the inequality that represents the situation of the question. Now let's solve it.

The condition placed can be fulfilled only if

$t+2\le 3$

And:

$t+2\ge -3$

Solving the first inequality:

$t\le 1$

And the second:

$t\ge -5$

This means the temperature can vary from -5°F to 1°F on the freezer