Đáp án:
a)$ x<\dfrac{35}{4}\\
b)
x\geq \dfrac{-59}{2}$
Giải thích các bước giải:
$a)x+1-\dfrac{x-1}{3}<\dfrac{2x+3}{2}+\dfrac{x}{3}+5\\
\Leftrightarrow x+1-\dfrac{x-1}{3}-\dfrac{2x+3}{2}-\dfrac{x}{3}-5<0\\
\Leftrightarrow x-\dfrac{x-1+x}{3}-\dfrac{2x+3}{2}-4<0\\
\Leftrightarrow x+\dfrac{2x-1}{3}-\dfrac{2x+3}{2}-4<0\\
\Leftrightarrow 6x+2(2x-1)-3(2x+3)-24<0\\
\Leftrightarrow 6x+4x-2-6x-9-24<0\\
\Leftrightarrow 4x-35<0\\
\Leftrightarrow x<\dfrac{35}{4}\\
b)
\dfrac{2x-3}{4}-\dfrac{x+1}{3}\leq \dfrac{1}{2}-\dfrac{3-x}{5}\\
\Leftrightarrow \dfrac{15(2x-3)}{15.4}-\dfrac{20.(x+1)}{20.3}\leq \dfrac{1.30}{30.2}-\dfrac{12.(3-x)}{12.5}\\
\Leftrightarrow 30x-45-20x-20\leq 30-36+12x\\
\Leftrightarrow 10x-65\leq -6+12x\\
\Leftrightarrow 10x-12x\leq -6+65\\
\Leftrightarrow -2x\leq 59\\
\Leftrightarrow x\geq \dfrac{-59}{2}$
