Question

solve the inequality and graph the solution.
10 + 3d < -2
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.
-5 -4 -3 -2 -1 0 1 2 3 4 5
submit

Explanation:

Step1: Subtract 10 from both sides

To isolate the term with \(d\), we subtract 10 from both sides of the inequality \(10 + 3d < -2\). This gives us \(10 + 3d - 10 < -2 - 10\), which simplifies to \(3d < -12\).

Step2: Divide both sides by 3

To solve for \(d\), we divide both sides of the inequality \(3d < -12\) by 3. Since 3 is a positive number, the direction of the inequality sign remains the same. So we have \(\frac{3d}{3} < \frac{-12}{3}\), which simplifies to \(d < -4\).

To graph the solution:

• The solution \(d < -4\) means we have an open circle at \(d = -4\) (because the inequality is strict, not including -4) and we shade the region to the left of -4 on the number line.

Answer:

The solution to the inequality is \(d < -4\). For the graph, place an open circle at \(-4\) and shade the line to the left of \(-4\).