To solve the inequality \( b - 88 - 1 \leq 86 \), we first simplify the left-hand side:
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Combine like terms on the left side: \[ b - 89 \leq 86 \]
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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
- Plot the Endpoint: Since \( b \leq 175 \), we plot the point 175 on a number line.
- 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.
- 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.