Bot GPT 4-o mini 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.
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