Question

\(\frac{15}{41}+\frac{-138}{41}\le x< \frac{1}{2}+\frac{1}{3}+\frac{1}{6}\)

Answer 1

\(\frac{15}{41}+\frac{-138}{41}\le x< \frac{1}{2}+\frac{1}{3}+\frac{1}{6}\)

\(\Leftrightarrow-3\le x< 1\)

\(\Leftrightarrow x\in\left\{-3;-2;-1;0\right\}\)

Answer 2

\(\frac{15}{41}+\frac{-138}{41}\le x< \frac{1}{2}+\frac{1}{3}+\frac{1}{6}\)

\(\Rightarrow\frac{15+(-138)}{41}\le x< \frac{1\cdot3}{6}+\frac{1\cdot2}{6}+\frac{1}{6}\)

\(\Rightarrow\frac{-123}{41}\le x< \frac{3}{6}+\frac{2}{6}+\frac{1}{6}\)

\(\Rightarrow-3\le x< 1\Leftrightarrow x\in\left\{-3;-2;-1;0\right\}\)

Answer 3

\(\frac{15}{41}+\frac{-138}{41}\le x< \frac{1}{2}+\frac{1}{3}+\frac{1}{6}\)

\(\Rightarrow-3\le x< 1\)

\(\Rightarrow x\in\left\{-3;-2;-1;0\right\}\)