Question

solve the inequality and graph the solution. 38(g - 6) < 76. 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: Solve the inequality

First, expand the left - hand side: $38(g - 6)=38g-228$. So the inequality becomes $38g - 228<76$.
Add 228 to both sides: $38g-228 + 228<76 + 228$, which simplifies to $38g<304$.
Divide both sides by 38: $\frac{38g}{38}<\frac{304}{38}$, so $g < 8$.

Step2: Graph the solution

On the number - line, we plot an open circle at 8 (because the inequality is strict, $g$ cannot equal 8) and draw a ray to the left of 8 to represent all values of $g$ that satisfy the inequality.

Answer:

The solution of the inequality is $g < 8$. On the number - line, there is an open circle at 8 and a ray extending to the left.