Question

Solve the inequality and graph the solution.
3–v<–1

Answer 1

To solve the inequality \( 3 - v < -1 \), follow these steps:

1. Subtract 3 from both sides of the inequality:
\[
-v < -1 - 3
\]
This simplifies to:
\[
-v < -4
\]

2. Multiply both sides of the inequality by -1. Remember, when multiplying or dividing by a negative number, we need to reverse the inequality sign:
\[
v > 4
\]

Thus, the solution to the inequality is \( v > 4 \).

**Graphing the Solution:**
The graph of \( v > 4 \) is represented on a number line:

- Draw a number line.
- Place an open circle (which signifies that 4 is not included in the solution) at 4.
- Shade the line to the right of 4 to indicate that all values greater than 4 are included in the solution.

\[
\text{Number Line:}
\]

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

The open circle at 4 and the shading to the right show that all numbers greater than 4 are solutions to the inequality.