Solve the inequality and graph the solution.

To solve the inequality \( 76 \geq 46 + 5r \), we can start by isolating \( r \).

1. Subtract 46 from both sides: \[ 76 - 46 \geq 5r \] \[ 30 \geq 5r \]

2. Next, divide both sides by 5: \[ \frac{30}{5} \geq r \] \[ 6 \geq r \] Which can also be written as: \[ r \leq 6 \]

The solution to the inequality is \( r \leq 6 \).

Graphing the Solution

To graph the solution \( r \leq 6 \):

• Draw a number line.
• Place a solid dot on the number 6 to indicate that 6 is included in the solution (since the inequality is "less than or equal to").
• Shade the line to the left of 6 to indicate all values less than 6 are included in the solution.

Here's a textual representation of what the graph would look like:

<---●============================>
     5   6   7   8   9 

The solid dot at 6 indicates that it is part of the solution, while the shaded line to the left shows all numbers less than 6 are included in the solution set.