Toán Lớp 7: Tìm x
|x-3/2|+|3/2-x|=2
|11/4-|x-3/2||=2
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Toán Lớp 7: Tìm x
|x-3/2|+|3/2-x|=2
|11/4-|x-3/2||=2
Comments ( 1 )
Ta có:
(x-3/2)+(3/2-x)
=x-3/2+3/2-x
=0
=>(x-3/2);(3/2-x)là 2 số đối nhau
=>|x-3/2|=|3/2-x|
=>|x-3/2|+|x-3/2|=2
=>2|x-3/2|=2
=>|x-3/2|=2:2
=>|x-3/2|=1
=>{(x-3/2=1),(x-3/2=-1):}
=>{(x=1+3/2),(x=-1+3/2):}
=>{(x=2/2+3/2),(x=-2/2+3/2):}
=>=>{(x=5/2),(x=1/2):}
Vậy x in{5/2;1/2}
=>{(11/4- |x-3/2|=2),(11/4- |x-3/2|=-2):}
=>{(|x-3/2|=11/4-2),(|x-3/2|=11/4+2):}
=>{(|x-3/2|=3/4),(|x-3/2|=19/4):}
=>{(x-3/2=3/4),(x-3/2=-3/4),(x-3/2=19/4),(x-3/2=-19/4):}
=>{(x=3/4+3/2),(x=-3/4+3/2),(x=19/4+3/2),(x=-19/4+3/2):}
=>{(x=9/4),(x=3/4),(x=25/4),(x=-13/4):}
Vậy x in{9/4;3/4;25/4;-13/4}