Question

solve the inequality and graph the solution.
65 > d + 73
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.
(number line from -10 to 10 with ticks at -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10)
submit

Explanation:

Step1: Subtract 73 from both sides

To solve the inequality \( 65 > d + 73 \), we subtract 73 from both sides of the inequality. This is done to isolate the variable \( d \) on one side.
\( 65 - 73 > d + 73 - 73 \)

Step2: Simplify both sides

Simplifying the left - hand side: \( 65-73=-8 \). Simplifying the right - hand side: \( d + 73-73=d \). So the inequality becomes \( - 8>d \), or equivalently \( d < - 8 \).

To graph the solution:

• We have an open circle at \( d=-8 \) because the inequality is strict ( \( d < - 8 \), not \( d\leq - 8 \)).
• Then we draw a ray to the left of \( - 8 \) on the number line to represent all the values of \( d \) that are less than \( - 8 \).

Answer:

The solution to the inequality \( 65>d + 73 \) is \( d < - 8 \). The graph has an open circle at \( - 8 \) and a ray extending to the left.