Question

Solve the inequality and graph the solution.

4x + 2 < 3x - 4

(1 point)
Responses

Answer 1

To solve the inequality \(4x + 2 < 3x - 4\), follow these steps:

1. **Isolate the variable:** Start by subtracting \(3x\) from both sides of the inequality.

\[
4x - 3x + 2 < -4
\]

This simplifies to:

\[
x + 2 < -4
\]

2. **Subtract 2 from both sides:**

\[
x < -4 - 2
\]

Simplifying gives:

\[
x < -6
\]

So the solution to the inequality is \(x < -6\).

### Graphing the Solution

To graph this inequality on a number line:

- Draw a number line.
- Place an open circle at \(-6\) to denote that \(-6\) is not included in the solution.
- Shade the line to the left of \(-6\) to indicate that all numbers less than \(-6\) are part of the solution.

Here's a representation of the graph:

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

Here, the parenthesis at \(-6\) indicates that \(-6\) itself is not included in the solution set.