To solve the inequality 82–d > 78, we need to isolate the variable d.
First, subtract 82 from both sides of the inequality:
82 - d - 82 > 78 - 82
Simplifying:
-d > -4
Next, divide both sides of the inequality by -1. Remember that when we divide/multiply by a negative number, the direction of the inequality sign flips:
-d/-1 < -4/-1
Simplifying:
d < 4
The solution to the inequality is d < 4.
To graph the solution, we will plot a ray starting from 4 on the number line. Since the inequality is strict (d < 4), we will use an open circle at 4 to represent that it does not include the number 4. Then, we will draw a ray extending to the left to represent all the numbers less than 4.
The graph will look like this:
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