Question

solve the inequality and graph the solution. 2 ≤ 3(r + 3) + 5 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.

Explanation:

Step1: Expand the right - hand side

First, expand $3(r + 3)+5$ using the distributive property. $3(r + 3)+5=3r+9 + 5=3r + 14$. So the inequality becomes $2\leq3r + 14$.

Step2: Subtract 14 from both sides

Subtract 14 from both sides of the inequality: $2-14\leq3r+14 - 14$. This simplifies to $- 12\leq3r$.

Step3: Divide both sides by 3

Divide both sides of the inequality $-12\leq3r$ by 3. We get $\frac{-12}{3}\leq\frac{3r}{3}$, which simplifies to $-4\leq r$ or $r\geq - 4$.

Answer:

The solution of the inequality is $r\geq - 4$. On the number - line, we plot a closed circle at $r=-4$ (because the inequality is $\geq$) and draw a ray to the right of $-4$.