Question

tìm x biết \(\left|2x+3\right|-2\left|4-x\right|=5\)

Answer 1

\(\left|2x+3\right|-2\left|4-x\right|=5\)

\(\Rightarrow\left|2x+3\right|-\left|2x-8\right|=5\)

+) Xét \(x\ge4\) có:

\(2x+3-2x+8=5\)

\(\Rightarrow11=5\) ( vô lí )

+) Xét \(\dfrac{-3}{2}\le x< 4\) có:
\(2x+3-8+2x=5\)

\(\Rightarrow4x=10\)

\(\Rightarrow x=2,5\) ( t/m )

+) Xét \(x< \dfrac{-3}{2}\) có:

\(-2x-3-8+2x=5\)

\(\Rightarrow5=5\) ( luôn đúng )

\(\Rightarrow x\in R\forall x< \dfrac{-3}{2}\)

Vậy x = 2,5 hoặc \(x\in R\forall x< \dfrac{-3}{2}\)