Question

solve the following inequality
b+6<7
2) Write the inequality using interval notation. Use "oo" (two lower case o's) for oo.
graph the solution set.
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Answer 1

To solve the inequality \( b + 6 < 7 \), we need to isolate \( b \). Here's how you can do it step by step:

1. Subtract 6 from both sides:
\[
b + 6 - 6 < 7 - 6
\]
\[
b < 1
\]

So the solution to the inequality is \( b < 1 \).

### Interval Notation
In interval notation, this is expressed as:
\[
(-\infty, 1)
\]

### Graphing the Solution Set
To graph this solution on a number line:

1. Draw a number line.
2. Put an open circle at \( 1 \) to indicate that \( 1 \) is not included in the solution.
3. Shade the line to the left of \( 1 \) to indicate all numbers less than \( 1 \).

Here's a simple representation of the graph:

```
<----|----|----|----|----|----|----|----|----|----|---->
-10 -5 0 1 2 3 4 5 6 7 8
(--------------------->
```

The open circle at \( 1 \) indicates \( b \) can take any value less than \( 1 \).