Solve for v. |v| - 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: |v| - 7 > -2 First, we isolate the absolute value term by adding 7 to both sides of the inequality. |v| - 7 + 7 > -2 + 7 |v| > 5Interpret absolute value: Now we interpret the absolute value inequality. The inequality |v| > 5 means that v is more than 5 units away from 0 on the number line. This leads to two separate inequalities: v > 5 or v 5 or v < -5

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Solve for $v$ . $\newline$ \lvert v \rvert - 7 > -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.

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Algebra 1

Solve absolute value inequalities

Full solution

Q. Solve for

v

\newline

\lvert v \rvert - 7 > -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.

Isolate absolute value: We have the inequality: $\newline$ |v| - 7 > -2 $\newline$ First, we isolate the absolute value term by adding $7$ to both sides of the inequality. $\newline$ |v| - 7 + 7 > -2 + 7 $\newline$ |v| > 5
Interpret absolute value: Now we interpret the absolute value inequality. $\newline$ The inequality |v| > 5 means that $v$ is more than $5$ units away from $0$ on the number line. This leads to two separate inequalities: $\newline$ v > 5 or v < -5
Write compound inequality: We can now write the compound inequality that represents the solution to the original inequality. $\newline$ The compound inequality is: $\newline$ v > 5 or v < -5