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

Solve Absolute Value Inequality: We have the inequality: |w - 6| ≥ 1 First, we need to solve for |w - 6|.Split into Two Inequalities: The absolute value inequality |w - 6| ≥ 1 means that the expression inside the absolute value, w - 6, is either greater than or equal to 1 or less than or equal to -1.Solve w - 6 ≥ 1: We can split the inequality into two separate inequalities: 1. w - 6 ≥ 1 2. w - 6 ≤ -1Solve w - 6 ≤ -1: Let's solve the first inequality: w - 6 ≥ 1 Add 6 to both sides: w ≥ 1 + 6 w ≥ 7Combine Inequalities: Now, let's solve the second inequality: w - 6 ≤ -1 Add 6 to both sides: w ≤ -1 + 6 w ≤ 5Final Solution: Combining both inequalities, we get the compound inequality: w ≤ 5 or w ≥ 7 This is the solution to the original inequality |w - 6| ≥ 1.

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Solve for $w$ . $\newline$ $|w - 6| \geq 1$ $\newline$ 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 - 6| \geq 1

\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

______

Solve Absolute Value Inequality: We have the inequality: $\newline$ $|w - 6| \geq 1$ $\newline$ First, we need to solve for $|w - 6|$ .
Split into Two Inequalities: The absolute value inequality $|w - 6| \geq 1$ means that the expression inside the absolute value, $w - 6$ , is either greater than or equal to $1$ or less than or equal to $-1$ .
Solve $w - 6 \geq 1$ : We can split the inequality into two separate inequalities: $\newline$ $1$ . $w - 6 \geq 1$ $\newline$ $2$ . $w - 6 \leq -1$
Solve $w - 6 \leq -1$ : Let's solve the first inequality: $w - 6 \geq 1$ Add $6$ to both sides: $w \geq 1 + 6$ $w \geq 7$
Combine Inequalities: Now, let's solve the second inequality: $\newline$ $w - 6 \leq -1$ $\newline$ Add $6$ to both sides: $\newline$ $w \leq -1 + 6$ $\newline$ $w \leq 5$
Final Solution: Combining both inequalities, we get the compound inequality: $\newline$ $w \leq 5$ or $w \geq 7$ $\newline$ This is the solution to the original inequality $|w - 6| \geq 1$ .