Question

giải bpt sau:

\(3x-\frac{x+2}{3}\le\frac{3\left(x-2\right)}{2}+5-x\)

Answer 1

\(3x-\frac{x+2}{3}\le\frac{3\left(x-2\right)}{2}+5-x\)

\(\Leftrightarrow\frac{18x}{6}-\frac{2\left(x+2\right)}{6}\le\frac{9\left(x-2\right)}{6}+\frac{30}{6}-\frac{6x}{6}\)

\(\Rightarrow18x-2x-4\le9x-18+30-6x\)

\(\Leftrightarrow16x-4\le3x+12\)

\(\Leftrightarrow13x\le16\)

\(\Leftrightarrow x\le\frac{16}{13}\)

Vậy bất phương trình có tập nghiệm là: \(S=\left\{x|x\le\frac{16}{13}\right\}\)