Question

How do you solve `|1- 2x | = 9`?

Answer 1

`x=-4`
`x=5`

Explanation:

First square both sides of the equation and then root both sides

`|1-2x|=9`

`(1-2x)^2=81`

`+-(1-2x)=9`

Then we would just solve it using two different routes.

`1-2x=9`

`2x=-8`

`x=-4`

`-1+2x=9`

`2x=10`

`x=5`

Answer 2

`x=-4" " or" "x=5`

Explanation:

If `absa=b" "`then `" "a=+b" "ora=-b`
`" "`
`abs(1-2x)=9`
`" "`
`1-2x=9" " or " "1-2x=-9`
`" "`
`1-2x=9`
`" "`
`rArr-2x=9-1`
`" "`
`rArr-2x=8`
`" "`
`rArrx=-8/2=-4`
`" "`
Or
`" "`
`1-2x=-9`
`" "`
`rArr-2x=-9-1`
`" "`
`rArr-2x=-10`
`" "`
`rArrx=(-10)/(-2)`
`" "`
`rArrx=5`
`" "`
Hence, `" "x=-4" "or" "x=5`