Solve for b. 6|b| ≤ 6 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Divide by 6: We have the inequality: 6|b| ≤ 6 First, we divide both sides of the inequality by 6 to isolate the absolute value of b. |b| ≤ 6/6 |b| ≤ 1Interpret absolute value: Now we interpret the absolute value inequality. The inequality |b| ≤ 1 means that b is within 1 unit of 0 on the number line. This can be written as two separate inequalities: -b ≤ 1 and b ≤ 1Rewrite -b ≤ 1: The inequality -b ≤ 1 can be rewritten by multiplying both sides by -1, remembering to reverse the inequality sign when multiplying by a negative number. b ≥ -1Combine inequalities: Combining the two inequalities, we get the compound inequality: -1 ≤ b ≤ 1 This is the final answer, which represents all values of b that are within 1 unit of 0 on the number line.

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Solve for $b$ . $\newline$ $6|b| \leq 6$ $\newline$ 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

b

\newline

6|b| \leq 6

\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

\_\_

Divide by $6$ : We have the inequality: $\newline$ $6|b| \leq 6$ $\newline$ First, we divide both sides of the inequality by $6$ to isolate the absolute value of $b$ . $\newline$ $|b| \leq \frac{6}{6}$ $\newline$ $|b| \leq 1$
Interpret absolute value: Now we interpret the absolute value inequality. $\newline$ The inequality $|b| \leq 1$ means that $b$ is within $1$ unit of $0$ on the number line. $\newline$ This can be written as two separate inequalities: $\newline$ $-b \leq 1$ and $b \leq 1$
Rewrite $-b \leq 1$ : The inequality $-b \leq 1$ can be rewritten by multiplying both sides by $-1$ , remembering to reverse the inequality sign when multiplying by a negative number. $\newline$ $b \geq -1$
Combine inequalities: Combining the two inequalities, we get the compound inequality: $\newline$ $-1 \leq b \leq 1$ $\newline$ This is the final answer, which represents all values of $b$ that are within $1$ unit of $0$ on the number line.