https://file.aiquickdraw.com/mathbot/file/1727412061023y3avzizv.jpg

The question asks to **"Gambarkan grafik"**, which translates to "Draw the graph" for each of the given inequalities or equations:

### a. \( y - 1 \leq x \leq y + 1 \)
This is an inequality describing a band of lines between two bounds:
1. \( x = y - 1 \) (a line with slope 1 and intercept -1)
2. \( x = y + 1 \) (a line with slope 1 and intercept 1)

The solution region is the area between these two lines.

### b. \( y = |1 - |x|| \)
This is a compound absolute value function. To break it down:
1. \( y = 1 - |x| \) gives a V-shaped graph inverted (since it opens downward) with a maximum at \( (0, 1) \).
2. It has an additional absolute value around the whole expression, which will reflect this V-shape upwards.

### c. \( y \leq |x| \)
This describes the region below the graph of \( y = |x| \), which is a V-shaped graph opening upwards.

### d. \( |y| < 2|x| \)
This represents two regions:
1. \( y < 2|x| \) and \( y > -2|x| \), which corresponds to a region between two lines: \( y = 2x \) and \( y = -2x \).

Would you like me to sketch these graphs or provide further clarification?

### Related Questions:
1. How do you solve absolute value inequalities in general?
2. How would the graph of \( y = |x - 1| \) differ from \( y = |x| \)?
3. What is the significance of absolute values when graphing linear inequalities?
4. How does reflecting a graph across the x-axis or y-axis affect its shape?
5. What are some common techniques for solving inequalities graphically?

**Tip:** When graphing inequalities, always shade the region representing the solution set.

Gambarkan grafik:
a. y - 1 ≤ x ≤ y + 1
b. y = |1 - |x||
c. y ≤ |x|
d. |y| < 2|x|

Explore how to graph algebraic inequalities involving absolute value functions, such as y - 1 ≤ x ≤ y + 1, y = |1 - |x||, y ≤ |x|, and |y| < 2|x|. Detailed explanations for solving and sketching these inequalities, suitable for Grades 9-11.

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