Question

solve the inequality: -3x + 4 > -2
options:
x < 2
x < -1
x > -1
x > 2

Explanation:

Step1: Subtract 4 from both sides

To isolate the term with \( x \), we subtract 4 from both sides of the inequality \(-3x + 4 > -2\). This gives us \(-3x + 4 - 4 > -2 - 4\), which simplifies to \(-3x > -6\).

Step2: Divide by -3 (reverse inequality)

When dividing both sides of an inequality by a negative number, we must reverse the inequality sign. Dividing both sides of \(-3x > -6\) by \(-3\) gives \( x < 2 \) (since \(\frac{-3x}{-3} < \frac{-6}{-3}\) simplifies to \( x < 2 \)).

Answer:

\( x < 2 \) (corresponding to the first option, e.g., if the first option is labeled with \( x < 2 \), then the answer is that option)