Question

Solve and graph this inequality: 5x -10 < 2x - 4

Answer 1

To solve the inequality \( 5x - 10 < 2x - 4 \), we can follow these steps:

1. **Isolate the variable term on one side**:
Start by getting all the \( x \) terms on one side and the constant terms on the other.

\[
5x - 2x < -4 + 10
\]

This simplifies to:

\[
3x < 6
\]

2. **Divide by 3**:
Divide both sides of the inequality by 3 to solve for \( x \).

\[
x < 2
\]

Now we have the solution: \( x < 2 \).

### Graphing the Inequality
To graph the inequality \( x < 2 \):

1. **Draw a number line**.
2. **Plot the point at 2** and use an open circle to indicate that 2 is not included in the solution (because it's a strict inequality).
3. **Shade the region to the left of 2** to indicate all the values of \( x \) that are less than 2.

Here's an illustration of that:

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

The shaded area extends to the left of 2, reflecting all values of \( x \) that are less than 2.