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

Rewrite the inequality: We have the inequality |v - 3| ≤ 5. We need to solve for v. The absolute value inequality |x| ≤ a means that -a ≤ x ≤ a. So, we can rewrite the inequality without the absolute value as two separate inequalities: -5 ≤ v - 3 ≤ 5.Solve for left part: We will first solve the left part of the inequality: -5 ≤ v - 3. We need to isolate v by adding 3 to both sides of the inequality. -5 + 3 ≤ v - 3 + 3 -2 ≤ vSolve for right part: Now we will solve the right part of the inequality: v - 3 ≤ 5. We need to isolate v by adding 3 to both sides of the inequality. v - 3 + 3 ≤ 5 + 3 v ≤ 8Combine results: Combining the results from Step 2 and Step 3, we get the compound inequality -2 ≤ v ≤ 8. This is the solution to the original absolute value inequality |v - 3| ≤ 5.

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Solve for $v$ . $\newline$ $\lvert v - 3 \rvert \leq 5$ $\newline$ 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

v

\newline

\lvert v - 3 \rvert \leq 5

\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

______

Rewrite the inequality: We have the inequality $|v - 3| \leq 5$ . We need to solve for $v$ . The absolute value inequality $|x| \leq a$ means that $-a \leq x \leq a$ . So, we can rewrite the inequality without the absolute value as two separate inequalities: $-5 \leq v - 3 \leq 5$ .
Solve for left part: We will first solve the left part of the inequality: $-5 \leq v - 3$ . We need to isolate $v$ by adding $3$ to both sides of the inequality. $\newline$ $-5 + 3 \leq v - 3 + 3$ $\newline$ $-2 \leq v$
Solve for right part: Now we will solve the right part of the inequality: $v - 3 \leq 5$ . We need to isolate $v$ by adding $3$ to both sides of the inequality. $\newline$ $v - 3 + 3 \leq 5 + 3$ $\newline$ $v \leq 8$
Combine results: Combining the results from Step $2$ and Step $3$ , we get the compound inequality $-2 \leq v \leq 8$ . This is the solution to the original absolute value inequality $|v - 3| \leq 5$ .