How do you solve the equation #abs(1-2x)=9#?

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Answer 1 · 2017-10-10T10:24:13

#x=5 " or "-4#

Rearranging equation, #abs(-2x+1)=9#

We know that either #−2x+1=9# or #−2x+1=−9#

For the #color(blue)("negative")# case:
#abs(-2x+1)=-(-2x+1)=9#

#=>+2x-1=9#

#=>+2x=9+1=10#

#=>x=10/2=5#

For the #color(red)("positive")# case:
#abs(-2x+1)=(-2x+1)=9#

#=>-2x=9-1=8#

So, #x=5 " or "-4#