Solve for v. |-2v| ≤ 6 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Identify Inequality: We have the inequality: |-2v| ≤ 6 First, we solve for |-2v|. |-2v| ≤ 6 This means that -2v must be greater than or equal to -6 and less than or equal to 6.Split Inequality: Now we split the inequality into two separate inequalities to remove the absolute value: -2v ≤ 6 and -2v ≥ -6Solve First Inequality: We solve the first inequality for v: -2v ≤ 6 Divide both sides by -2, remembering to reverse the inequality sign because we are dividing by a negative number: v ≥ -3Solve Second Inequality: We solve the second inequality for v: -2v ≥ -6 Divide both sides by -2, again reversing the inequality sign: v ≤ 3Combine Inequalities: Now we combine both inequalities to get the compound inequality: -3 ≤ v ≤ 3 This is the solution to the original problem.

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Solve for $v$ . $\newline$ $\lvert -2v \rvert \leq 6$ $\newline$ 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 2

Solve absolute value inequalities

Full solution

Q. Solve for

v

\newline

\lvert -2v \rvert \leq 6

\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.

Identify Inequality: We have the inequality: $\newline$ $|-2v| \leq 6$ $\newline$ First, we solve for $|-2v|$ . $\newline$ $|-2v| \leq 6$ $\newline$ This means that $-2v$ must be greater than or equal to $-6$ and less than or equal to $6$ .
Split Inequality: Now we split the inequality into two separate inequalities to remove the absolute value: $\newline$ $-2v \leq 6$ and $-2v \geq -6$
Solve First Inequality: We solve the first inequality for $v$ : $-2v \leq 6$ Divide both sides by $-2$ , remembering to reverse the inequality sign because we are dividing by a negative number: $v \geq -3$
Solve Second Inequality: We solve the second inequality for $v$ : $-2v \geq -6$ Divide both sides by $-2$ , again reversing the inequality sign: $v \leq 3$
Combine Inequalities: Now we combine both inequalities to get the compound inequality: $\newline$ $-3 \leq v \leq 3$ $\newline$ This is the solution to the original problem.