Question

the owner of a butcher shop keeps the shop's freezer at -5°C. It is acceptable for the temperature to differ from this value by 1.5°. Write and solve an absolute-value equation to find minimum and maximum acceptable temperatures

Answer 1

`|x+5|=1.5`

is the equation describing minimum and maximum acceptable temperatures.

The minimum temperature could be
`-6.5^(\circ)`

and the maximum temperature could be
`-3.5^(\circ)`

Explanation:

The owner of a butcher shop keeps the shop's freezer at -5°C. It is acceptable for the temperature to differ from this value by 1.5°. So, the minimum temperature could be

`-5^(\circ)-1.5^(\circ)=-6.5^(\circ)`

and the maximum temperature could be

`-5^(\circ)+1.5^(\circ)=-3.5^(\circ)`

Let
`x^(\circ)` be acceptable temperature of freezer. The difference between the acceptable temperature and given temperature
`x-(-5)=x+5` cannot be more than 1.5° and less than 1.5°, so

`|x+5|\le 1.5`

Then

`|x+5|=1.5`

is the equation describing minimum and maximum acceptable temperatures.

Solve it:

`x+5=1.5\text{ or }x+5=-1.5\\ \\x=1.5-5\text{ or }x=-1.5-5\\ \\x=-3.5\text{ or }x=-6.5`