Question

How do you graph and solve `|2x – 3| – 6 = –1`?

Answer 1

`-1=x=4`

Explanation:

When you have an absolute value equation, you isolate the absolute value before trying anything else.
`|2x-3|-6=-1` becomes
`|2x-3|=5`
We have to note that there are two solutions to absolute value equations, since `|-a|=a` and `|a|=a`
In other words, `2x-3=5` and `2x-3=-5` both give you the final answer of `|2x-3|=5`.
`2x-3=5`
`2x=8`
`x=4`

`2x-3=-5`
`2x=-2`
`x=-1`
When we plug in these values, we find out that they both work. Therefore, `-1=x=4`