Question

Solve the given inequality and represent its solution on the number line. 18-6x>-12

Answer 1

To solve the inequality \( 18 - 6x > -12 \), follow these steps:

1. **Isolate the term involving \( x \)**:

Subtract \( 18 \) from both sides:
\[
18 - 6x - 18 > -12 - 18
\]
This simplifies to:
\[
-6x > -30
\]

2. **Divide by -6**:

When dividing or multiplying both sides of an inequality by a negative number, the inequality sign must be flipped:
\[
x < 5
\]

So the solution to the inequality \( 18 - 6x > -12 \) is:
\[
x < 5
\]

### Number Line Representation:

To represent this solution on a number line:

- Draw a number line.
- Mark the point \( 5 \) on the line.
- Since \( x \) is less than \( 5 \), use an open circle at \( 5 \) (indicating that \( 5 \) is not included in the solution) and shade the line to the left of \( 5 \).

Here's a visual representation:

```
<---|----|----|----|----|----|----|----|----|----|----|--->
1 2 3 4 5 6 7 8 9 10
(open circle at 5)
```

The shaded portion to the left of \( 5 \) indicates all values of \( x \) that are less than \( 5 \).