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Solve for $d$ . $|{-2d}| \geq 2$ 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

d

.

|{-2d}| \geq 2

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.

\_\_\_\_\_

Split into Two Cases: Now, we split it into two cases because the absolute value can represent either a positive or negative inside value. $\newline$ Case $1$ : $-2d \geq 2$ $\newline$ Case $2$ : $-2d \leq -2$
Solve Case $1$ : Let's solve Case $1$ . $\newline$ $-2d \geq 2$ $\newline$ Divide both sides by $-2$ , remembering to flip the inequality sign because we're dividing by a negative number. $\newline$ $d \leq -1$
Solve Case $2$ : Now, let's solve Case $2$ . $\newline$ $-2d \leq -2$ $\newline$ Divide both sides by $-2$ , again flipping the inequality sign. $\newline$ $d \geq 1$
Combine Cases: Combine both cases into a compound inequality. $\newline$ $d \leq -1$ or $d \geq 1$

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