Give a unique example of each:
1. Part 1: An absolute value equation with two solutions
2. Part 2: An absolute value equation with one solution
3. Part 3: An absolute value equation with no solutions

Question

anonymous · Answer

1.
$$|x|=3$$
meaning $$x=\ \pm 3$$

anonymous · Answer

$$|x|=-2$$

anonymous · Answer

for part 3

anonymous · Answer

$$|2x+5|=4x-8$$
$$2x+5=4x-8$$
$$13=2x$$
$$13/2=x$$

$$|2x+5|=4x-8$$
$$2x+5=-(4x-8)$$
$$2x+5=-4x+8$$
$$6x=3$$
$$x=\frac{1}{2}$$

anonymous · Answer

|x| = 3 (2 solutions -3 and +3)
|x| = 0 (x can only be 0)
|x| = -5 (An absolute value can never be negative)