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

Question

-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.