Solve for b. |b| - 7 ≤ 2 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Isolate absolute value: We have the inequality: |b| - 7 ≤ 2 First, we need to isolate the absolute value term |b| on one side of the inequality.Add 7: Add 7 to both sides of the inequality to isolate |b|: |b| - 7 + 7 ≤ 2 + 7 |b| ≤ 9Consider absolute value definition: Now we need to consider the definition of absolute value, which states that |b| is the distance of b from 0 on the number line. The inequality |b| ≤ 9 means that b is within a distance of 9 from 0. This gives us two scenarios: b is less than or equal to 9 and b is greater than or equal to -9.Translate into compound inequality: Translate the definition of absolute value into a compound inequality: -b ≤ 9 and b ≤ 9 Since -b ≤ 9 is equivalent to b ≥ -9, we can write the compound inequality as: -9 ≤ b ≤ 9

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Solve for $b$ . $\newline$ $|b| - 7 \leq 2$ $\newline$ 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

|b| - 7 \leq 2

\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 absolute value: We have the inequality: $\newline$ $|b| - 7 \leq 2$ $\newline$ First, we need to isolate the absolute value term $|b|$ on one side of the inequality.
Add $7$ : Add $7$ to both sides of the inequality to isolate $|b|$ : $\newline$ $|b| - 7 + 7 \leq 2 + 7$ $\newline$ $|b| \leq 9$
Consider absolute value definition: Now we need to consider the definition of absolute value, which states that |b|\(\newline) is the distance of b\(\newline) from \(0 $\newline$ ) on the number line. The inequality |b| \leq \(9 $\newline$ ) means that b\(\newline) is within a distance of \(9 $\newline$ ) from \(0 $\newline$ ). This gives us two scenarios: b \leq \(9 $\newline$ ) and b \geq \(-9 $\newline$ ).
Translate into compound inequality: Translate the definition of absolute value into a compound inequality: $\newline$ $-b \leq 9$ and $b \leq 9$ $\newline$ Since $-b \leq 9$ is equivalent to $b \geq -9$ , we can write the compound inequality as: $\newline$ $-9 \leq b \leq 9$