Question

Solve for x and graph the solution on the number line below. the number line goes from -12 all the way to 12, please include how I should color the number line, 1≥x/3

Answer 1

To solve the inequality \( 1 \geq \frac{x}{3} \), we start by rewriting it in a more standard form.

1. Multiply both sides of the inequality by 3 to eliminate the fraction. Remember that since we are multiplying by a positive number, the direction of the inequality does not change:

\[
1 \cdot 3 \geq x
\]

This simplifies to:

\[
3 \geq x
\]

or equivalently:

\[
x \leq 3
\]

Now, let's summarize what this means. The solution set describes all values of \( x \) that are less than or equal to 3.

2. To graph this on a number line that extends from -12 to 12:
- Mark the point \( x = 3 \) on the number line.
- Since the inequality is \( x \leq 3 \), we use a closed dot (or filled circle) at \( 3 \) to indicate that \( 3 \) is included in the solution.
- Color the portion of the number line to the left of \( 3 \) (including \( 3 \)) to indicate that all these values satisfy the inequality.

Here’s how the number line will look:

- **Closed dot at 3** (indicating that \( 3 \) is included)
- **Arrow or shading from -12 to 3** (indicating all values less than or equal to 3)

In summary:
- The solution to the inequality is \( x \leq 3 \).
- Graphically, you would represent this by shading from -12 to 3, with a filled circle at 3.

Answer 2

and what's the Inequality Notation?

Answer 3

The inequality notation for the solution you found, which states that \( x \) is less than or equal to \( 3 \), is:

\[
x \leq 3
\]

This notation indicates that \( x \) can take any value that is less than or equal to \( 3 \).