Solve,graph,and check

12<6x+b

To solve the inequality 12 < 6x + b, we need to isolate the variable x on one side of the inequality symbol. Let's start by subtracting b from both sides:

12 - b < 6x

Next, divide both sides of the inequality by 6:

(12 - b) / 6 < x

The inequality sign remains the same since we are dividing by a positive number.

Now, let's graph this inequality. Since we have a strict inequality, the graph will be represented by a dashed line. To determine the direction of the inequality, we need to know the value of b. If b is positive, the inequality will be graphed as an open circle to the left of the line. If b is negative, the open circle will be on the right of the line.

Additionally, since x can take any value less than (12 - b) / 6, we'll shade the area to the left of the line.

After graphing, you will have a dashed line with an open circle on one end and shading towards the other end.

To check if a specific value satisfies the inequality, substitute it into the original inequality and see if the statement is true.