Question

The heat in the house is set to keep the minimum and maximum temperatures (in degrees Fahrenheit) according to the equation |x – 72.5| = 4. What are the minimum and maximum temperatures in the house?72.5°F and 76.5°F68.5°F and 76.5°F70.5°F and 74.5°F72.5°F and 74.5°F

Answer 1

Given the equation $|x-72.5|=4$.

When x is maximum, we have

$|x-72.5|= x-72.5$. Hence $x-72.5 =4\\x=76.5$

The maximum temperature is $76.5\; ^oF$

When x is minimum, we have

$|x-72.5|=72.5-x$. Hence $72.5-x =4\\x=68.5$

The minimum temperature is $68.5\; ^oF$

Answer 2

Answer:

Therefore the minimum and maximum temperature in the house are 68.5°F and 76.5°F respectively

Step-by-step explanation:

Given the equation that relates the minimum and maximum temperature of heat of a house as;

|x – 72.5| = 4

Since the function at the left hand side is an absolute value, the equation can be expressed in two ways because the modulus function can either be a negative function (for minimum temperature) or positive function (maximum temperature).

The equation can be rewritten the following ways;

-(x-72.5) = 4 ...1 OR

x-72.5 = 4 ... 2

Solving equation 1 to get x;

-x+72.5 = 4

-x = 4-72.5

-x = -68.5

x = 68.5°F (minimum temperature)

Solving equation 2 for x;

x-72.5 = 4

x = 4+72.5

x = 76.5°F (maximum temperature)

Therefore the minimum and maximum temperature in the house are 68.5°F and 76.5°F respectively