Question

solve the inequality and graph the solution. 15 < 3(g + 5) + 9 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

Explanation:

Step1: Simplify the right side

First, expand and simplify \(3(g + 5)+9\). Using the distributive property \(a(b + c)=ab+ac\), we get \(3g+15 + 9\), then combine like terms: \(3g+24\). So the inequality becomes \(15<3g + 24\).

Step2: Subtract 24 from both sides

Subtract 24 from each side to isolate the term with \(g\). \(15-24<3g+24 - 24\), which simplifies to \(-9<3g\).

Step3: Divide by 3

Divide both sides by 3 to solve for \(g\). \(\frac{-9}{3}<\frac{3g}{3}\), so \(- 3-3\)).

To graph the solution: On the number line, we have an open circle at \(-3\) (since the inequality is strict, \(g
eq - 3\)) and we shade the region to the right of \(-3\) to represent all values of \(g\) greater than \(-3\).

Answer:

The solution to the inequality is \(g > - 3\). For the graph, there is an open circle at \(-3\) and the line is shaded to the right of \(-3\).