Solve the inequality and graph the solution.

Question

b–88
–
1
≤86
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 \( b - 88 - 1 \leq 86 \), we first simplify the left-hand side:

1. Combine like terms on the left side: \[ b - 89 \leq 86 \]

2. Next, add 89 to both sides to isolate \( b \): \[ b \leq 86 + 89 \] \[ b \leq 175 \]

The solution to the inequality is: \[ b \leq 175 \]

This means \( b \) can take values that are less than or equal to 175.

Graphing the Solution

1. Plot the Endpoint: Since \( b \leq 175 \), we plot the point 175 on a number line.
2. Choose the Endpoint Type: Since the inequality includes \( b = 175 \), we will use a closed circle to indicate that this point is included in the solution.
3. Middle to Delete: We will shade to the left to indicate all values less than or equal to 175, which means we do not include positions to the right of 175.

Graph:

• Closed circle at 175.
• Shaded line/range extending to the left.

Here's a simple representation of the number line graphically:

<---|----------------0---|----------------|------------>
   0              175

• The closed circle at \( 175 \) indicates that \( b = 175 \) is included in the solution.
• The shaded area extends indefinitely to the left, indicating all numbers less than 175 are included.