Question

Bài 3.4: Tìm x, biết:

a) \(\left|2x-5\right|=x+1\)

b) \(\left|3x-2\right|-1=x\)

c) \(\left|3x-7\right|=2x+1\)

d) \(\left|2x-1\right|-1=x\)

Answer 1

a) \(\left|2x-5\right|=x+1\)

+) Xét \(x\ge\frac{5}{2}\) có:

\(2x-5=x+1\)

\(\Rightarrow x=6\) ( t/m )

+) Xét \(x< \frac{5}{2}\) có:
\(-\left(2x-5\right)=x+1\)

\(\Rightarrow-2x+5=x+1\)

\(\Rightarrow-3x=-4\)

\(\Rightarrow x=\frac{4}{3}\) ( t/m )

Vậy \(x\in\left\{6;\frac{4}{3}\right\}\)

b) \(\left|3x-2\right|-1=x\)

+) Xét \(x\ge\frac{2}{3}\) có:
\(3x-2-1=x\)

\(\Rightarrow2x=3\)

\(\Rightarrow x=\frac{3}{2}\) ( t/m )

+) Xét \(x< \frac{2}{3}\) có:
\(2-3x-1=x\)

\(\Rightarrow1=4x\)

\(\Rightarrow x=\frac{1}{4}\) ( t/m )

Vậy \(x\in\left\{\frac{3}{2};\frac{1}{4}\right\}\)

Các phần c, d tương tự