Question

Give a unique example of each:

An absolute value equation with two solutions
An absolute value equation with one solution
An absolute value equation with no solutions

Answer 1

a) |x|=1

Answer 2

b) |x| = 0

Answer 3

a unique example lol

Answer 4

c) |x| = -1

Answer 5

what would be another one for c?

Answer 6

|x| = i (where i = sqrt(-1))

Answer 7

how about a, a number tho

Answer 8

@ybarrap

Answer 9

Any negative number. Recall that absolute value must be greater than or equal to 0.

Answer 10

x=-13 ?

Answer 11

|x|=-13, yes, this has no solutions.

Answer 12

how about for B

Answer 13

or A

Answer 14

Think about the graph of the absolute value of x:

Answer 15

ok?

Answer 16

If you want to find an equation where |x|=y has no solutions, draw a horizontal line that doesn't intersect the graph:

Answer 17

ok what about with two solutions

Answer 18

And the same principle applies if we want to find a value of x where theres only one solution. Where on this graph can you draw a horizontal line that intersects only once?

And where can you draw a horizontal line that intersects twice?

Answer 19

what about x=3

Answer 20

Don't forget your absolute value bars, |x|=3. That would look like this

Answer 21

so it would work for two solutions

Answer 22

Yep, exactly. You can use your graph to help you.

Answer 23

what other than 0 can we get one solution?

Answer 24

0 is the only way to get one solution, because you can't draw a horizontal line that intersects the graph exactly once, except 0

Answer 25

ok thats what i thought

Answer 26

Think of absolute value as a mapping of a function to the positive value of itself, so -1 goes to 1, -100 goes to 100 and 100 of course goes to 100

Answer 27

0 goes to zero but |x| = 1, can take 1 to 1 but also -1 to 1, so there are two solutions, but zero doesn't have a negative partner

Answer 28

oh ok

Answer 29

thank youuu

Answer 30

You're welcome, glad I could help