Solve for r. 7|r| ≥ 7 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Isolate |r|: We have the inequality: 7|r| ≥ 7 First, we divide both sides by 7 to isolate |r|. 7|r| / 7 ≥ 7 / 7 Split into Two Inequalities: The absolute value inequality |r| ≥ 1 can be split into two separate inequalities: r ≥ 1 or r ≤ -1 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: r ≥ 1 or r ≤ -1 This is the final answer in the form of a compound inequality.

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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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Algebra 1

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

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.