Question

olve the following inequality. Justify each step.
negative 4 less than or equals StartFraction t Over 7 EndFraction
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Part 1
What is the​ solution?
  
enter your response here
​(Simplify your answer. Type an​ inequality.)

Answer 1

To solve the inequality \(-4 \leq \frac{t}{7}\), follow these steps:

1. **Multiply both sides by 7**: Since 7 is positive, the direction of the inequality remains the same.

\[
-4 \times 7 \leq \frac{t}{7} \times 7
\]

This simplifies to:

\[
-28 \leq t
\]

2. **Rearranging the inequality**: The result can also be written as:

\[
t \geq -28
\]

So, the solution to the inequality is:

\[
t \geq -28
\]

This means that \(t\) can take any value greater than or equal to \(-28\).