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.