To solve the inequality \(-4 \leq \frac{t}{7}\), let's follow the steps clearly and justify each step taken:
Step 1: Eliminate the fraction
To eliminate the fraction, we will multiply both sides of the inequality by 7. However, since we are multiplying by a positive number, the direction of the inequality remains the same.
\[ -4 \times 7 \leq \frac{t}{7} \times 7 \]
This simplifies to:
\[ -28 \leq t \]
or equivalently:
\[ t \geq -28 \]
Final Solution
So, the solution to the inequality is:
\[ t \geq -28 \]
Part 2: Properties of Inequalities Used
In the solution process, we used the following property of inequalities:
D. Division property of inequality
This is because we were effectively dividing both sides by 7 to isolate \(t\), although in this specific case, we multiplied instead of dividing to eliminate the fraction. The division property states that if \( a \leq b \) and \( c > 0 \), then \( \frac{a}{c} \leq \frac{b}{c} \).
Since we multiplied by a positive number, other properties were not necessary for this case (we did not need addition or subtraction properties).
Therefore:
- The correct property used in the manipulation is: D. Division property of inequality