Question

solve the inequality and graph the solution. 16 > 3(b - 1) + 7. 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 $3(b - 1)+7$ using the distributive property. $3(b - 1)+7=3b-3 + 7=3b + 4$. So the inequality becomes $16>3b + 4$.

Step2: Isolate the term with the variable

Subtract 4 from both sides of the inequality. $16-4>3b+4 - 4$, which simplifies to $12>3b$.

Step3: Solve for b

Divide both sides of the inequality by 3. $\frac{12}{3}>\frac{3b}{3}$, so $4>b$ or $b < 4$.

Step4: Graph the solution

On the number - line, plot an open circle at 4 (because the inequality is $b < 4$, not $b\leq4$) and draw a ray to the left of 4.

Answer:

The solution of the inequality is $b < 4$. On the number - line, there is an open circle at 4 and a ray extending to the left.