Solve the inequality and graph the solution.

Question

52(t+5)≤
–
52
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality \( 52(t + 5) \leq -52 \), follow these steps:

1. Distribute: \[ 52t + 260 \leq -52 \]

2. Subtract 260 from both sides: \[ 52t \leq -52 - 260 \] \[ 52t \leq -312 \]

3. Divide by 52: \[ t \leq \frac{-312}{52} \] This simplifies to: \[ t \leq -6 \]

So, the solution to the inequality is: \[ t \leq -6 \]

Graphing the solution:

• Endpoint: The endpoint of the interval is \( -6 \).
• Closed circle: Since the inequality is "less than or equal to," we will use a closed circle at \( -6 \).
• Line/shade: Shade to the left of \( -6 \) to indicate all values less than \( -6 \).

Summary of the graph:

1. Plot a closed circle at \(-6\).
2. Shade the area to the left of \(-6\) to indicate all values less than or equal to \(-6\).

Here's a simple representation of how the graph would look:

<---●====================== (Graphical representation of the solution)
      -8  -7  -6  -5  -4

In this graph, the closed circle at \(-6\) indicates that \(-6\) is included in the solution, and the shaded line to the left shows that all values less than \(-6\) are also included.