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Solve for $r$ . $\newline$ 8|r| > 16 $\newline$ 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. $\newline$ ______

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Solve absolute value inequalities

Full solution

Q. Solve for

r

.

\newline

8|r| > 16

\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.

\newline

______

Divide by $8$ : We have the inequality: $\newline$ 8|r| > 16 $\newline$ First, we divide both sides of the inequality by $8$ to isolate $|r|$ . $\newline$ \frac{8|r|}{8} > \frac{16}{8} $\newline$ |r| > 2
Interpret absolute value: Now we interpret the absolute value inequality |r| > 2. $\newline$ This means $r$ is either greater than $2$ or less than $-2$ . $\newline$ So we can write two separate inequalities: $\newline$ r > 2 or r < -2
Express as compound inequality: We now express the solution as a compound inequality. The compound inequality is: r < -2 or r > 2

More problems from Solve absolute value inequalities

Question

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Write a compound inequality like

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

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\newline

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\newline

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Question

t

\newline

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\newline

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Question

p

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

\newline

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Question

v

\newline

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\newline

Write a compound inequality like

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

\newline

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