Solve the following inequality. Justify each step.

Question

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 \( -4 \leq \frac{t}{7} \), we will follow these steps:

1. Eliminate the fraction: Multiply both sides of the inequality by 7. Since 7 is a positive number, the direction of the inequality remains the same.

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

   This simplifies to:

   \[ -28 \leq t \]

   or you may also write it as:

   \[ t \geq -28 \]

2. Write the solution: The final solution is:

   \[ t \geq -28 \]

So the solution to the inequality is \( t \geq -28 \).