Question

1. solve the inequality: $-4v + 2v > 6$

a. $v < -1$
b. $v > -1$
c. $v < -3$
d. $v > -20$

Explanation:

Step1: Combine like terms

First, we combine the terms with \( v \) on the left side of the inequality. \(-4v + 2v\) can be simplified. Since \(-4v + 2v = (-4 + 2)v\), we calculate \(-4 + 2 = -2\). So the inequality becomes \(-2v > 6\).

Step2: Solve for \( v \)

To solve for \( v \), we divide both sides of the inequality by \(-2\). When we divide or multiply both sides of an inequality by a negative number, the direction of the inequality sign changes. So dividing both sides of \(-2v > 6\) by \(-2\) gives \( v < \frac{6}{-2}\). Calculating \(\frac{6}{-2} = -3\), we get \( v < -3 \).

Answer:

C. \( v < -3 \)