Solve for r. |r - 8| ≥ 8 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Absolute Value Inequality: We have the inequality |r - 8| ≥ 8. The absolute value inequality means that the expression inside the absolute value, r - 8, can either be greater than or equal to 8 or less than or equal to -8.Case 1: r - 8 ≥ 8: First, let's solve for the case where r - 8 is greater than or equal to 8: r - 8 ≥ 8 Add 8 to both sides to isolate r: r - 8 + 8 ≥ 8 + 8 r ≥ 16Case 2: r - 8 ≤ -8: Now, let's solve for the case where r - 8 is less than or equal to -8: r - 8 ≤ -8 Add 8 to both sides to isolate r: r - 8 + 8 ≤ -8 + 8 r ≤ 0Compound Inequality Solution: Combining both cases into a compound inequality, we get: r ≤ 0 or r ≥ 16 This is the solution to the inequality |r - 8| ≥ 8.

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Solve for $r$ . $|r - 8| \geq 8$ 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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Algebra 1

Solve absolute value inequalities

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Q. Solve for

r

|r - 8| \geq 8

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

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

Absolute Value Inequality: We have the inequality $|r - 8| \geq 8$ . The absolute value inequality means that the expression inside the absolute value, $r - 8$ , can either be greater than or equal to $8$ or less than or equal to $-8$ .
Case $1$ : $r - 8 \geq 8$ : First, let's solve for the case where $r - 8$ is greater than or equal to $8$ : $r - 8 \geq 8$ Add $8$ to both sides to isolate $r$ : $r - 8 + 8 \geq 8 + 8$ $r \geq 16$
Case $2$ : $r - 8 \leq -8$ : Now, let's solve for the case where $r - 8$ is less than or equal to $-8$ : $r - 8 \leq -8$ Add $8$ to both sides to isolate $r$ : $r - 8 + 8 \leq -8 + 8$ $r \leq 0$
Compound Inequality Solution: Combining both cases into a compound inequality, we get: $\newline$ $r \leq 0$ or $r \geq 16$ $\newline$ This is the solution to the inequality $|r - 8| \geq 8$ .