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

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kudzordzifrancis

Answer:

Minimum: 3

Maximum: 13

Step-by-step explanation:

Georgia uses the equation

5 = |8 – x| to find the maximum and minimum values.

We solve the equation for x.

[tex]5 = |8 - x| [/tex]

By the definition of the absolute value function, we must have:

[tex] - 5 = 8 - x \: or \: 5 = 8 - x[/tex]

We subtract 8 from both sides to get:

[tex] - 5 - 8 = - x \: or \: 5 - 8 = - x[/tex]

[tex] - 13 = - x \: or \: - 3 = - x[/tex]

This simplifies to:

[tex]13 = x \: or \: 3 = x[/tex]

Therefore the minimum value is 3 and maximum is 13

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