Question

What are the values of m when |2m – 2| = 5

Answer 1

Answers: The solutions are m = 7/2 and m = -3/2

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Explanation:

$\text{If } |x| = k, \text{ then } x = k \text{ or } x = -k, \text{ where } k > 0$

Use that rule to break up the absolute value into two equations. Then solve each equation for m.

$|2m-2| = 5\\\\2m-2 = 5 \ \text{ or } \ 2m-2 = -5\\\\2m = 5+2 \ \text{ or } \ 2m = -5+2\\\\2m = 7 \ \text{ or } \ 2m = -3\\\\m = 7/2 \ \text{ or } \ m = -3/2$

Notes:

• 7/2 = 3.5
• -3/2 = -1.5