Question

What steps should be followed in order to solve the inequality statement?

-3t + 7 ≥ 9

add 7, multiply by -3, and flip the inequality symbol
subtract 7, divide by -3, and keep the inequality symbol
subtract 7, divide by -3, and flip the inequality symbol
add 7, multiply by -3, and keep the inequality symbol

Answer 1

To solve the inequality \(-3t + 7 ≥ 9\), we should follow these steps:

1. **Subtract 7 from both sides** to isolate the term involving the variable:
\[
-3t + 7 - 7 ≥ 9 - 7 \implies -3t ≥ 2
\]

2. **Divide by -3** to solve for \(t\). However, remember that when you divide (or multiply) both sides of an inequality by a negative number, you must **flip the inequality symbol**:
\[
t ≤ \frac{2}{-3} \implies t ≤ -\frac{2}{3}
\]

Given the options provided, the correct one that aligns with these steps is:

**subtract 7, divide by -3, and flip the inequality symbol.**