Question

solve the inequality. -2d - 2 < 3d + 8
solution:
graph the solution.

Explanation:

Step1: Move variable terms to one - side

Add \(2d\) to both sides of the inequality \(-2d - 2<3d + 8\). We get \(-2d+2d - 2<3d+2d + 8\), which simplifies to \(-2 < 5d+8\).

Step2: Move constant terms to the other - side

Subtract 8 from both sides: \(-2-8 < 5d+8 - 8\), resulting in \(-10 < 5d\).

Step3: Solve for \(d\)

Divide both sides by 5: \(\frac{-10}{5}<\frac{5d}{5}\), so \(d>- 2\).

Answer:

\(d > - 2\); For the graph, we use an open - circle at \(-2\) (since the inequality is strict, \(d
eq - 2\)) and an arrow pointing to the right on the number line.