Solve the inequality and graph the solution.

Question

2(b+6)+6<10
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.

Answer 1

Let's solve the inequality step by step.

Given the inequality: $$2(b+6)+6<10$$

First, distribute the $2$: $$2b+12+6<10$$ Combine like terms: $$2b+18<10$$

Next, subtract $18$ from both sides: $$2b<10-18$$ $$2b<-8$$

Now, divide both sides by $2$: $$b<-4$$

The solution to the inequality is: $$b<-4$$

Graphing the solution:

1. Endpoints: The endpoint is $-4$.
2. Open/Closed endpoint: Since the inequality is strictly less than ($<$), we will use an open circle at $-4$.
3. Middle of segment: The solution is a ray going to the left from $-4$.

Final Graph:

On a number line:

• Place an open circle at $-4$.
• Shade to the left to indicate that all values less than $-4$ are part of the solution.

The graph looks like this:

<---( -4 )--------------------------------------------------->

Here, the open circle at $-4$ indicates that $-4$ itself is not included in the solution. The shaded area to the left signifies all numbers less than $-4$ are included in the solution.