Solve for b. |3b| ≤ 9 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Given Inequality: We have the inequality: |3b| ≤ 9 First, we need to solve for |3b|. |3b| ≤ 9 This means that 3b is less than or equal to 9 and greater than or equal to -9.Split Inequality: Now we split the inequality into two separate inequalities because the absolute value of a number is the distance from zero, and it can be either positive or negative. So we have: 3b ≤ 9 and -3b ≤ 9Solve First Inequality: Let's solve the first inequality: 3b ≤ 9 Divide both sides by 3 to isolate b: b ≤ 9 / 3 b ≤ 3Solve Second Inequality: Now let's solve the second inequality: -3b ≤ 9 Divide both sides by -3. Remember that dividing by a negative number reverses the inequality sign: b ≥ 9 / -3 b ≥ -3Combine Inequalities: Combining both inequalities, we get the compound inequality: -3 ≤ b ≤ 3 This is the solution to the inequality |3b| ≤ 9.

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Solve for $b$ . $\newline$ $|3b| \leq 9$ $\newline$ 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

|3b| \leq 9

\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

______

Given Inequality: We have the inequality: $\newline$ $|3b| \leq 9$ $\newline$ First, we need to solve for $|3b|$ . $\newline$ $|3b| \leq 9$ $\newline$ This means that $3b$ is less than or equal to $9$ and greater than or equal to $-9$ .
Split Inequality: Now we split the inequality into two separate inequalities because the absolute value of a number is the distance from zero, and it can be either positive or negative. $\newline$ So we have: $\newline$ $3b \leq 9$ and $-3b \leq 9$
Solve First Inequality: Let's solve the first inequality: $\newline$ $3b \leq 9$ $\newline$ Divide both sides by $3$ to isolate $b$ : $\newline$ $b \leq \frac{9}{3}$ $\newline$ $b \leq 3$
Solve Second Inequality: Now let's solve the second inequality: $\newline$ $-3b \leq 9$ $\newline$ Divide both sides by $-3$ . Remember that dividing by a negative number reverses the inequality sign: $\newline$ $b \geq \frac{9}{-3}$ $\newline$ $b \geq -3$
Combine Inequalities: Combining both inequalities, we get the compound inequality: $\newline$ $-3 \leq b \leq 3$ $\newline$ This is the solution to the inequality $|3b| \leq 9$ .