To solve the inequality \(-5x \leq 25 - 5x\), we can start by simplifying it.
- First, add \(5x\) to both sides to eliminate \(-5x\) on the left side:
\[ -5x + 5x \leq 25 - 5x + 5x \]
This simplifies to:
\[ 0 \leq 25 \]
This statement (0 ≤ 25) is always true.
Since the inequality holds true for all values of \(x\), the solution set is all real numbers.
Part 1: Solution Set
The solution set can be expressed as:
\[ \text{StartSet } x ,|, x \in \mathbb{R} \text{ EndSet} \]
or simply:
\[ \mathbb{R} \]
Graphing the Solution Set:
To graph this inequality, you would represent the entire number line, indicating that all values of \(x\) satisfy the inequality:
- Draw a horizontal line to represent the number line.
- Shade the entire line to show that all real numbers are included in the solution set.
Conclusion:
The solution to the inequality \(-5x \leq 25 - 5x\) is all real numbers, and it can be represented graphically by shading the entire number line.
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