Solve for w. |w| + 7 > 17 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Isolate absolute value: We have the inequality: |w| + 7 > 17 First, we isolate |w| by subtracting 7 from both sides of the inequality. |w| + 7 - 7 > 17 - 7 |w| > 10 Interpret absolute value: Now we interpret the absolute value inequality |w| > 10. This means that w is either greater than 10 or less than -10. So we can write two separate inequalities: w > 10 or w 10 or w < -10 This is the final answer in the form of a compound inequality.

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Solve for $w$ . $\newline$ |w| + 7 > 17 $\newline$ 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

w

\newline

|w| + 7 > 17

\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: $\newline$ |w| + 7 > 17 $\newline$ First, we isolate $|w|$ by subtracting $7$ from both sides of the inequality. $\newline$ |w| + 7 - 7 > 17 - 7 $\newline$ |w| > 10
Interpret absolute value: Now we interpret the absolute value inequality |w| > 10. This means that $w$ is either greater than $10$ or less than $-10$ . So we can write two separate inequalities: w > 10 or w < -10
Final compound inequality: We now have the compound inequality that represents the solution to the original problem: $\newline$ w > 10 or w < -10 $\newline$ This is the final answer in the form of a compound inequality.