Question

\(\dfrac{x-1}{2}\)-\(\dfrac{7x+3}{15}\)\(\le\)\(\dfrac{2x+1}{3}\)+\(\dfrac{3-2x}{5}\)

Answer 1

\(\Leftrightarrow\dfrac{15\left(x-1\right)-2\left(7x+3\right)-10\left(2x+1\right)-6\left(3-2x\right)}{30}\le0\)

\(\Leftrightarrow15x-15-14x-6-20x+10-18+12x\le0\)

\(\Leftrightarrow-7x-29\le0\)

\(\Leftrightarrow-7x\le29\)

\(\Leftrightarrow x\ge-\dfrac{29}{7}\)

Answer 2

\(\dfrac{x-1}{2}-\dfrac{7x+3}{15}\le\dfrac{2x+1}{3}+\dfrac{3-2x}{5}\)

\(\Leftrightarrow\dfrac{15\left(x-1\right)}{30}-\dfrac{2\left(7x+3\right)}{30}\le\dfrac{10\left(2x+1\right)}{30}+\dfrac{6\left(3-2x\right)}{30}\)

\(\Leftrightarrow15x-15-14x-6\le20x+10+18-12x\)

\(\Leftrightarrow x-21\le8x+28\)

\(\Leftrightarrow x-8x\le28+21\)

\(\Leftrightarrow-7x\le49\)

\(\Leftrightarrow x\ge-7\)

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