Question

Georgia has a budget of $8 for a new notebook. she wants to spend within $5 of her budget, so she uses the equation 0 = |8 − x| − 5 to find the maximum and minimum values. what are the solutions to the equation?

Answer 1

The solutions to the equation 5 = | 8 - x| is 3 and 13.

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution.

For a new notepad, Georgia has allotted $8. She uses the formula 5 = |8 - x| to get the upper and lower bounds of her spending limit, which is $5.

Consider the equation,

5 = |8 – x|

When the Modulus is positive.

We have,

5 = |8 – x|

5 = 8 – x

Subtracting 8 from each side,

- x = - 3

x = 3

When the Modulus is negative.

We have,

5 = |8 – x|

5 = - ( 8 - x)

5 = - 8 + x

Adding 8 on each side of the equation,

x = 13

Therefore, the solution to the equation is 3 and 13.

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