Question

tìm x biết: |2x+3| = x+2

Answer 1

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

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

2x + 3 - x = 2 , 2x +3 \(_{\ge}\)0

-( 2x + 3 ) - x = 2 , 2x+ 3 <0

x = -1 , x \(\ge\)\(\dfrac{-3}{2}\)

x = \(\dfrac{-5}{3}\),x < - \(\dfrac{3}{2}\)

x = -1

x = - \(\dfrac{5}{3}\)

Answer 2

-1

Answer 3

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

\(\Rightarrow\left\{{}\begin{matrix}2x+3=x+2\\2x+3=-x+2\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}2x-x=2-3\\2x+x=2-3\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x=-1\\3x=-1\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x=-1\\x=\dfrac{-1}{3}\end{matrix}\right.\)

Answer 4

Lời giải

| 2x + 3 | = x + 2 (1)

Do \(VT\ge0\forall x\Rightarrow VP\ge0\Leftrightarrow x\ge-2\)

+Với 2x + 3 < 0 ; (1) trở thành: \(-2x-3=x+2\Leftrightarrow3x=-5\Leftrightarrow x=-\dfrac{5}{3}\)

+Với 2x + 3 \(\ge0\) ;(1) trở thành: \(2x+3=x+2\Leftrightarrow x=-1\)