Tìm x biết |x-2| = x+6

a,

+, Xét \(x\ge2\) ta có:

\(\left|x-2\right|=x-2\)

\(\Rightarrow x-2=x+6\Rightarrow0x=8\Rightarrow x\in\varnothing\)

+, Xét \(x< 2\) ta có:

\(\left|x-2\right|=2-x\)

\(\Rightarrow2-x=x+6\Rightarrow-2x=4\Rightarrow x=-2\)

(chọn vì thoả mãn điều kiện x<2)

b, Tương tự câu a.

c, +, Xét \(x\ge-\dfrac{3}{2}\) ta có:

\(\left|x\right|=-x;\left|2x-3\right|=2x-3\)

\(\Rightarrow-x-\left(2x-3\right)=x-1\)

\(\Rightarrow-x-2x-3-x=-1\)

\(\Rightarrow-4x=2\Rightarrow x=-\dfrac{1}{2}\)

(chọn vì thoả mãn điều kiện \(x\ge-\dfrac{3}{2}\))

+, Xét \(x< -\dfrac{3}{2}\) ta có:

\(\left|x\right|=-x;\left|2x+3\right|=-2x-3\)

\(\Rightarrow-x-\left(-2x-3\right)=x-1\)

\(\Rightarrow-x+2x+3-x=1\Rightarrow0x=-2\Rightarrow x\in\varnothing\)

+, Xét \(x\ge0\) ta có:

\(\left|x\right|=x;\left|2x+3\right|=-2x-3\)

\(\Rightarrow x-\left(-2x-3\right)=x-1\)

\(\Rightarrow x+2x+3-x=-1\)

\(\Rightarrow2x=2\Rightarrow x=1\)

+, Xét \(x< 0\) ta có:

\(\left|x\right|=-x;\left|2x+3\right|=-2x-3\)

\(\Rightarrow-x-\left(-2x-3\right)=x-1\)

\(\Rightarrow-x+2x-x=-1-3\Rightarrow0x=-4\Rightarrow x\in\varnothing\)

Vậy.............

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