Bài 1.
a.\(x-1< 3\)
\(\Leftrightarrow x< 4\)
b.\(-3x\ge6\)
\(\Leftrightarrow x\le2\)
Bài 2.
a.\(3-2x>4\)
\(\Leftrightarrow-2x>1\)
\(\Leftrightarrow x< -\dfrac{1}{2}\)
b.\(\dfrac{4x-5}{3}>\dfrac{7-x}{5}\)
\(\Leftrightarrow\dfrac{5\left(4x-5\right)}{15}>\dfrac{3\left(7-x\right)}{15}\)
\(\Leftrightarrow5\left(4x-5\right)>3\left(7-x\right)\)
\(\Leftrightarrow20x-25>21-3x\)
\(\Leftrightarrow23x>46\)
\(\Leftrightarrow x>2\)
c.\(\left(x-3\right)^2< x^2-3\)
\(\Leftrightarrow x^2-6x+9< x^2-3\)
\(\Leftrightarrow-6x< -12\)
\(\Leftrightarrow x>2\)
Bài 3.
a.\(\left|5x\right|=3x+8\)
\(ĐK:x\ge-\dfrac{8}{3}\)
\(\Leftrightarrow\left[{}\begin{matrix}5x=3x+8\\-5x=3x+8\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=4\left(tm\right)\\x=-1\left(tm\right)\end{matrix}\right.\)
b.\(\left|x+2\right|=2x-10\)
\(ĐK:x\ge5\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=2x-10\\-x-2=2x-10\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=12\left(tm\right)\\x=\dfrac{8}{3}\left(ktm\right)\end{matrix}\right.\)