To solve the inequality \(-4 \leq \frac{t}{7}\), follow these steps:
- Multiply both sides by 7: Since we're multiplying by a positive number, the direction of the inequality does not change. \[ -4 \cdot 7 \leq \frac{t}{7} \cdot 7 \] This simplifies to: \[ -28 \leq t \] or equivalently, \[ t \geq -28 \]
Solution: The solution is \(t \geq -28\).
Part 2: Properties of Inequalities Used
In this case, the relevant property is:
- D. Division property of inequality (since you essentially multiplied both sides by 7, which is indeed a form of scaling the inequality).
However, since we used multiplication (and multiplication is essentially a quicker way to think of division in context here), we can say:
- C. Multiplication property of inequality is also correct.
So for clarity, you would select:
- C. Multiplication property of inequality.
The other options (A. Subtraction and B. Addition) are not used in this solution.