Question

Solve the inequality and graph the solution.

4x + 2 3x - 4

(1 point)
Responses

Answer 1

To solve the inequality \( 4x + 2 < 3x - 4 \), let's start by isolating \( x \).

1. Subtract \( 3x \) from both sides:
\[
4x - 3x + 2 < -4
\]
This simplifies to:
\[
x + 2 < -4
\]

2. Next, subtract \( 2 \) from both sides:
\[
x < -4 - 2
\]
This simplifies to:
\[
x < -6
\]

Now we have the solution to the inequality, which is \( x < -6 \).

### Graphing the Solution:

To graph this inequality on a number line:
1. Draw a number line.
2. Mark the point \( -6 \).
3. Since the inequality is \( < \), draw an open circle at \( -6 \) to indicate that \( -6 \) is not included in the solution.
4. Shade the area to the left of \( -6 \) to indicate all values less than \( -6 \).

The final representation on the number line would look like this:

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

Here, the open circle at \( -6 \) indicates that \( -6 \) is not included in the solution, while the shading to the left shows all numbers less than \( -6 \).