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Solve for $c$ . $|{-2c}| > 6$ Write a compound inequality like $1 < x < 3$ or like $x < 1$ or $x > 3$ . Use integers, proper fractions, or improper fractions in simplest form. $\_\_\_\_\_$

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Solve absolute value inequalities

Full solution

Q. Solve for

c

.

|{-2c}| > 6

Write a compound inequality like

1 < x < 3

or like

x < 1

or

x > 3

. Use integers, proper fractions, or improper fractions in simplest form.

\_\_\_\_\_

Consider Cases: Now, we need to consider the two cases for the absolute value inequality. $\newline$ Case $1$ : $-2c > 6$ $\newline$ Case $2$ : $-2c < -6$
Solve Case $1$ : Let's solve Case $1$ . $\newline$ $-2c > 6$ $\newline$ Divide both sides by $-2$ , remembering to flip the inequality sign because we're dividing by a negative number. $\newline$ $c < -3$
Solve Case $2$ : Now, let's solve Case $2$ . $\newline$ $-2c < -6$ $\newline$ Divide both sides by $-2$ , no need to flip the inequality sign this time because we're dividing by a negative number. $\newline$ $c > 3$

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