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Solve for $d$ . $\newline$ -|d| < -20 $\newline$ 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

.

\newline

-|d| < -20

\newline

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.

Isolate absolute value term: We have the inequality: $\newline$ -|d| < -20 $\newline$ First, we need to isolate the absolute value term. To do this, we can divide both sides of the inequality by $-1$ , remembering that dividing by a negative number reverses the inequality sign. $\newline$ -|d| / -1 > -20 / -1
Divide by $-1$ : After dividing by $-1$ , we get: $\newline$ |d| > 20 $\newline$ This means that $d$ is greater than $20$ or less than $-20$ .
Write compound inequality: Now we can write the compound inequality. Since |d| > 20, $d$ can either be greater than $20$ or less than $-20$ . This gives us two inequalities: $\newline$ d > 20 or d < -20

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