Solve for w. |w| + 1 ≤ 5 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Isolate absolute value term: We have the inequality: |w| + 1 ≤ 5 First, we isolate the absolute value term by subtracting 1 from both sides of the inequality. |w| + 1 - 1 ≤ 5 - 1 |w| ≤ 4Interpret absolute value inequality: Now we interpret the absolute value inequality. The inequality |w| ≤ 4 means that w is at most 4 units away from 0 on the number line. This gives us two inequalities: w ≤ 4 and -w ≤ 4Solve for w: We solve the second inequality for w. -w ≤ 4 can be multiplied by -1 to reverse the inequality sign (remember that multiplying or dividing by a negative number reverses the inequality). -w * -1 ≥ 4 * -1 w ≥ -4Combine into compound inequality: Now we combine the two inequalities into a compound inequality. The solution to |w| ≤ 4 is that w is greater than or equal to -4 and less than or equal to 4. -4 ≤ w ≤ 4

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Solve for $w$ . $\newline$ $|w| + 1 \leq 5$ $\newline$ 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

w

\newline

|w| + 1 \leq 5

\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 term: We have the inequality: $\newline$ $|w| + 1 \leq 5$ $\newline$ First, we isolate the absolute value term by subtracting $1$ from both sides of the inequality. $\newline$ $|w| + 1 - 1 \leq 5 - 1$ $\newline$ $|w| \leq 4$
Interpret absolute value inequality: Now we interpret the absolute value inequality. The inequality $|w| \leq 4$ means that $w$ is at most $4$ units away from $0$ on the number line. This gives us two inequalities: $w \leq 4$ and $-w \leq 4$
Solve for $w$ : We solve the second inequality for $w$ . $-w \leq 4$ can be multiplied by $-1$ to reverse the inequality sign (remember that multiplying or dividing by a negative number reverses the inequality). $-w \times -1 \geq 4 \times -1$ $w \geq -4$
Combine into compound inequality: Now we combine the two inequalities into a compound inequality. $\newline$ The solution to $|w| \leq 4$ is that $w$ is greater than or equal to $-4$ and less than or equal to $4$ . $\newline$ $-4 \leq w \leq 4$