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

Identify Inequality: We have the inequality: |-8b| ≥ 8 First, we solve for |-8b|. |-8b| ≥ 8 This means that -8b is either greater than or equal to 8 or less than or equal to -8.Split into Cases: Now we split the inequality into two cases: Case 1: -8b ≥ 8 Case 2: -8b ≤ -8Solve Case 1: For Case 1, we divide both sides by -8 to solve for b, remembering to flip the inequality sign because we are dividing by a negative number: -8b ≥ 8 b ≤ -1Solve Case 2: For Case 2, we again divide both sides by -8, flipping the inequality sign: -8b ≤ -8 b ≥ 1Combine Cases: Combining both cases, we get the compound inequality: b ≤ -1 or b ≥ 1 This is the solution to the inequality.

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Solve for $b$ . $\newline$ $|-8b| \geq 8$ $\newline$ 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 2

Solve absolute value inequalities

Full solution

Q. Solve for

b

\newline

|-8b| \geq 8

\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

______

Identify Inequality: We have the inequality: $\newline$ $|-8b| \geq 8$ $\newline$ First, we solve for $|-8b|$ . $\newline$ $|-8b| \geq 8$ $\newline$ This means that $-8b$ is either greater than or equal to $8$ or less than or equal to $-8$ .
Split into Cases: Now we split the inequality into two cases: $\newline$ Case $1$ : $-8b \geq 8$ $\newline$ Case $2$ : $-8b \leq -8$
Solve Case $1$ : For Case $1$ , we divide both sides by $-8$ to solve for $b$ , remembering to flip the inequality sign because we are dividing by a negative number: $\newline$ $-8b \geq 8$ $\newline$ $b \leq -1$
Solve Case $2$ : For Case $2$ , we again divide both sides by $-8$ , flipping the inequality sign: $\newline$ $-8b \leq -8$ $\newline$ $b \geq 1$
Combine Cases: Combining both cases, we get the compound inequality: $\newline$ $b \leq -1$ or $b \geq 1$ $\newline$ This is the solution to the inequality.