Solve for v. -5|v| > -10 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Divide and Reverse Inequality: We have the inequality: -5|v| > -10 First, we divide both sides by -5 to isolate |v|. Remember that dividing by a negative number reverses the inequality sign. -5|v| / -5 < -10 / -5 |v| < 2 Interpret Absolute Value Inequality: Now we interpret the absolute value inequality |v| < 2. This means that v is less than 2 units away from 0 on the number line, so v can be between -2 and 2, but not including -2 and 2 because the inequality is strict (not ≤ or ≥). -2 < v < 2 Write Compound Inequality: We have now solved for v and can write the compound inequality as: -2 < v < 2 This is the final answer in the form of a compound inequality.

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Solve for $v$ . $\newline$ -5|v| > -10 $\newline$ 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

v

\newline

-5|v| > -10

\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

______

Divide and Reverse Inequality: We have the inequality: $\newline$ -5|v| > -10 $\newline$ First, we divide both sides by $-5$ to isolate $|v|$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ -5|v| / -5 < -10 / -5 $\newline$ |v| < 2
Interpret Absolute Value Inequality: Now we interpret the absolute value inequality |v| < 2. This means that $v$ is less than $2$ units away from $0$ on the number line, so $v$ can be between $-2$ and $2$ , but not including $-2$ and $2$ because the inequality is strict (not $\leq$ or $v$ $0$ ). $v$ $1$
Write Compound Inequality: We have now solved for $v$ and can write the compound inequality as: -2 < v < 2 This is the final answer in the form of a compound inequality.