To solve the inequality [tex]\(\frac{g+2}{-3} < -2\)[/tex], follow these detailed steps:
1. Multiply both sides by -3:
- When you multiply or divide an inequality by a negative number, you must reverse the direction of the inequality.
- Multiply both sides of the inequality [tex]\(\frac{g+2}{-3} < -2\)[/tex] by -3:
[tex]\[
\left(\frac{g+2}{-3}\right) \cdot (-3) > (-2) \cdot (-3)
\][/tex]
- This simplifies to:
[tex]\[
g + 2 > 6
\][/tex]
- Note that the less-than sign changes to a greater-than sign because we are multiplying by a negative number.
2. Subtract 2 from both sides:
- To isolate [tex]\(g\)[/tex], subtract 2 from both sides of the inequality:
[tex]\[
g + 2 - 2 > 6 - 2
\][/tex]
- This simplifies to:
[tex]\[
g > 4
\][/tex]
Hence, the correct sequence of steps is:
- Multiply both sides of the inequality by -3.
- Change the direction of the inequality.
- Subtract 2 from both sides of the inequality.
So, the answer is:
Multiply both sides of the inequality by -3. Change the direction of the inequality. Subtract 2 from both sides of the inequality.
