Question

Solve for x and graph the solution on the number line below.
x
−3≥
−4+x
Answer

A:<B:>C: ≤ D: ≥ E: or
Inequality Notation:
Number Line:——————————————
-12. -10. -8. -6 -4. -2. -0 2. 4. 6. 8. 10. 12

Answer 1

To solve the inequality:

\[
x - 3 \ge -4 + x
\]

First, we can simplify the inequality by subtracting \(x\) from both sides:

\[
x - x - 3 \ge -4 + x - x
\]

This simplifies to:

\[
-3 \ge -4
\]

Since \(-3\) is indeed greater than \(-4\), this inequality is always true. Thus, there is no restriction on \(x\).

The solution in inequality notation is:

\[
x \in (-\infty, \infty)
\]

This means all real numbers are a solution.

### Graph on the Number Line:

For the number line graph, since all real numbers are solutions, you would represent this by shading the entire line:

```
Number Line:
<-------------------------------------------------->
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
```

You can denote infinity at both ends if necessary, though it's generally implied when shading the entire number line.