a) \(\left|x\right|=1005\)
\(\Rightarrow\) x = 1005 hoặc x = -1005
b) \(\left|x\right|\) + 15 = 22 ; x > 0
x > 0 \(\Rightarrow\)\(\left|x\right|=x\)
\(\Rightarrow\left|x\right|+15=22\)
\(\Rightarrow x+15=22\)
\(\Rightarrow x=22-15\)
\(\Rightarrow x=7\)
c) \(\left|x\right|+12=25;x< 0\)
\(x< 0\Rightarrow\left|x\right|=-x\)
\(\Rightarrow\left|x\right|+12=25\)
\(\Rightarrow-x+12=25\)
\(\Rightarrow-x=25-12\)
\(\Rightarrow-x=13\)
\(\Rightarrow x=-13\)
d) \(\left|3x-15\right|=0\)
\(\Rightarrow3x-15=0\)
\(\Rightarrow3x=0+15\)
\(\Rightarrow3x=15\)
\(\Rightarrow x=15:3\)
\(\Rightarrow x=5\)
e) \(\left|-x+2\right|=4\)
\(\Rightarrow-x+2=4\) hoặc \(-x+2=-4\)
TH1: \(-x+2=4\)
\(-x=4-2\)
\(-x=2\)
\(\Rightarrow x=-2\)
TH2: \(-x+2=-4\)
\(-x=-4-2\)
\(-x=-6\)
\(\Rightarrow x=6\)
f) \(\left|-x+\left|31-\left(-89\right)\right|\right|=14\)
\(\Rightarrow\left|-x+\left|120\right|\right|=14\)
\(\Rightarrow\left|-x+120\right|=14\)
\(\Rightarrow-x+120=14\) hoặc \(-x+120=-14\)
TH1: \(-x+120=14\)
\(\Rightarrow-x=14-120\)
\(\Rightarrow-x=-106\)
\(\Rightarrow x=106\)
TH2: \(-x+120=-14\)
\(\Rightarrow-x=-14-120\)
\(\Rightarrow-x=-134\)
\(\Rightarrow x=134\)
