Question

Answer 1

\(\Leftrightarrow\dfrac{12\left(2x-5\right)+10\left(x-3\right)-14x-15}{15}< 0\)

\(\Leftrightarrow24x-60+10x-30-14x-15< 0\)

\(\Leftrightarrow20x-105< 0\)

\(\Leftrightarrow20x< 105\)

\(\Leftrightarrow x< \dfrac{21}{4}\)

Answer 2

\(\Leftrightarrow\dfrac{12\left(2x-5\right)+10\left(x-3\right)-14x-15}{15}\)< 0

\(\Leftrightarrow24x-60+10x-30-14x-15\) < 0

\(\Leftrightarrow20x< 105\)

\(\Leftrightarrow x< \dfrac{21}{4}\)

Answer 3

\(\dfrac{4\left(2x-5\right)}{5}+\dfrac{2\left(x-3\right)}{3}< \dfrac{14x}{15}+1\) 
\(\Leftrightarrow\dfrac{12\left(2x-5\right)}{15}+\dfrac{10\left(x-3\right)}{15}< \dfrac{14x}{15}+\dfrac{15}{15}\\ \Leftrightarrow12\left(2x-5\right)+10\left(x-3\right)< 14x+15\\ \Leftrightarrow24x-60+10x-30< 14x+15\\ \Leftrightarrow34x-90< 14x+15\\ \Leftrightarrow34x-14x< 15+90\\ \Leftrightarrow20x< 105\\ \Leftrightarrow x< 5,25\)