Question

Solve for v. |v|–7gt; – 1 Write a compound inequality like 1 lt; x lt; 3 or like x lt; 1 or x gt; 3. Use integers, proper fractions, or improper fractions in simplest form.

A) v>6 AND v<−6
B) v>6 OR v<−6
C) v≥6 OR v≤−6
D) v>6 AND v≤−6

Answer 1

The inequality |v| - 7 > -1 results in a compound inequality solution of v > 6 OR v < -6, which corresponds to answer option B.

Step-by-step explanation:

To solve the inequality |v| - 7 > -1, we will consider two cases because the absolute value of v (|v|) could be either positive or negative.

Case 1: If v is non-negative (v ≥ 0), we have v - 7 > -1. Adding 7 to both sides gives us v > 6.

Case 2: If v is negative (v < 0), we have -v - 7 > -1. Adding 7 to both sides and then multiplying by -1 gives us v < -6 (don't forget to reverse the inequality when you multiply or divide by a negative number).

Combining both cases, we have a compound inequality: v > 6 OR v < -6. This indicates that v is either greater than 6 or less than -6.

Therefore, the correct answer is B) v > 6 OR v < -6.