Risolvere le seguenti disequazioni:

1) $3x\leq 4$;

$\displaystyle \frac{3x}{3}\leq \frac{4}{3}$;

$\displaystyle x\leq \frac{4}{3}$

$\displaystyle S=\{ x\in \mathbb{R} \:| x\leq \frac{4}{3}\}$

2) $-x>3$;

$x<-3$

$\displaystyle S=\{x\in \mathbb{R} \:| x<-3\}$

3) $-5x\geq 3$;

$5x\leq -3$;

$\displaystyle \frac{5x}{5}\leq -\frac{3}{5}$;

$\displaystyle x \leq -\frac{3}{5}$;

$\displaystyle S=\{x\in \mathbb{R} \:| x\leq-\frac{3}{5}\}$

4) $2x>4$;

$\displaystyle \frac{2x}{2}> \frac{4}{2}$;

$\displaystyle x> 2$

$\displaystyle  S=\{x\in \mathbb{R} \:| x>2\}$

5) $5(x-3)<3(x+2)+2x-3$;

$5x-15<3x+6+2x-3$;

$5x-3x-2x<15+ 6-3$;

$0<18$ disequazione sempre verificata, ovvero $S=\mathbb{R}$