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Solve for $r$ . $\newline$ $7|r| \geq 7$ $\newline$ 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

7|r| \geq 7

\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

______

Isolate $|r|$ : We have the inequality: $\newline$ $7|r| \geq 7$ $\newline$ First, we divide both sides by $7$ to isolate $|r|$ . $\newline$ $\frac{7|r|}{7} \geq \frac{7}{7}$ $\newline$ $|r| \geq 1$
Split into Two Inequalities: The absolute value inequality $|r| \geq 1$ can be split into two separate inequalities: $\newline$ $r \geq 1$ or $r \leq -1$ $\newline$ This is because the absolute value of $r$ is greater than or equal to $1$ if $r$ is either greater than or equal to $1$ or less than or equal to $-1$ .
Write Compound Inequality: We write the compound inequality as requested: $\newline$ $r \geq 1$ or $r \leq -1$ $\newline$ This is the final answer in the form of a compound inequality.

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