Question

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

Answer 1

1.
\[|x|=3\]
meaning \[x=\ \pm 3\]

Answer 2

\[|x|=-2\]

Answer 3

for part 3

Answer 4

\[|2x+5|=4x-8\]
\[2x+5=4x-8\]
\[13=2x\]
\[13/2=x\]

\[|2x+5|=4x-8\]
\[2x+5=-(4x-8)\]
\[2x+5=-4x+8\]
\[6x=3\]
\[x=\frac{1}{2}\]

Answer 5

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