Question
Choose the true statement about the graph of \( x-1 \leq 2 \) closed circle on 1 and all numbers to the left shaded
Ask by Mitchell Rose. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The graph has a closed circle at 3 and shades all numbers to the left of 3.
Solution
To analyze the inequality \( x - 1 \leq 2 \), we can solve it step by step.
1. **Isolate \( x \)**:
\[
x - 1 \leq 2
\]
Add 1 to both sides:
\[
x \leq 3
\]
2. **Interpret the inequality**:
The solution \( x \leq 3 \) means that \( x \) can take any value less than or equal to 3.
3. **Graph the inequality**:
- A closed circle (or dot) is placed at \( x = 3 \) to indicate that 3 is included in the solution set.
- The shading will extend to the left of 3, indicating all values less than 3 are included.
Thus, the true statement about the graph of \( x - 1 \leq 2 \) is that there is a closed circle on 3, and all numbers to the left of 3 are shaded.
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Simplify this solution Extra Insights
The graph of the inequality \( x-1 \leq 2 \) can be simplified to \( x \leq 3 \). This represents all numbers less than or equal to 3. In this case, you would draw a closed circle on 3 and shade everything to the left. Remember, the closed circle indicates that 3 is included in the solution set! If you mistakenly interpret \( x-1 \leq 2 \) as \( x-1 < 2 \), you would misplace your circle and shading! So, double-check the inequality before graphing; it can change everything! Always ensure you're accurately translating inequalities into their graphical counterparts!
