Question

solve the inequality and graph the solution. 3(b - 6) < 6. 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 left - hand side

$3(b - 6)=3b-18$, so the inequality becomes $3b - 18<6$.

Step2: Add 18 to both sides

$3b-18 + 18<6 + 18$, which simplifies to $3b<24$.

Step3: Divide both sides by 3

$\frac{3b}{3}<\frac{24}{3}$, resulting in $b < 8$.

Answer:

The solution of the inequality is $b < 8$. On the number - line, we use an open circle at $b = 8$ (since the inequality is strict, $b$ cannot equal 8) and draw an arrow to the left to represent all values of $b$ that satisfy the inequality.