Question

1. what is the solution set for $\frac{-6x + 4}{7} > -2$?

options: $x > \frac{5}{3}$, $x < \frac{5}{3}$, $x < 3$, $x > 3$

Explanation:

Step1: Multiply both sides by 7

$$\frac{-6x+4}{7} \times 7 > -2 \times 7$$
$$-6x + 4 > -14$$

Step2: Subtract 4 from both sides

$$-6x + 4 - 4 > -14 - 4$$
$$-6x > -18$$

Step3: Divide by -6, flip inequality

$$\frac{-6x}{-6} < \frac{-18}{-6}$$
$$x < 3$$

Answer:

$\boldsymbol{x < 3}$ (Option: $\boldsymbol{x < 3}$)