Question

Giải các bất phương trình:

\(a,\left(x+1\right)\left(2x-3\right)< 0\)

\(b,\frac{x+5}{6}+\frac{x-1}{3}\le\frac{x+3}{2}-1\)

Answer 1

\(b,\frac{x+5}{6}+\frac{x-1}{3}\le\frac{x+3}{2}-1.\)

\(\Rightarrow\frac{x+5}{6}+\frac{2\left(x-1\right)}{6}\le\frac{x+3}{2}-1\)

\(\Rightarrow\frac{x+5}{6}+\frac{2x-2}{6}\le\frac{x+3}{2}-1\)

\(\Rightarrow\frac{x+5+2x-2}{6}\le\frac{x+3}{2}-1\)

\(\Rightarrow\frac{3x+3}{6}\le\frac{3\left(x+3\right)}{6}-\frac{6}{6}\)

\(\Rightarrow\frac{3x+3}{6}\le\frac{3x+9}{6}-\frac{6}{6}\)

\(\Rightarrow\frac{3x+3}{6}\le\frac{3x+9-6}{6}\)

\(\Rightarrow\frac{3x+3}{6}\le\frac{3x+3}{6}\)

\(\Rightarrow3x+3\le3x+3\)

\(\Rightarrow S=\varnothing\)