Esercizi sui sistemi di disequazione

Per th0JL7QJCF risolvere i sistemi di disequazione è sufficiente essere in grado di risolvere le disequazioni lineari e ricordarsi che la soluzione viene data dalla regione in cui entrambe contemporaneamente risolvono le rispettive disequazioni di partenza.

Per un livello minimo (6)

6.1. $\left\{\begin{matrix} x-3>0\\x-2>0 \end{matrix}\right.$	$\left [ x>3 \right ]$
6.2. $\left\{\begin{matrix} x-5<0\\x-6>0 \end{matrix}\right.$	$\left [ S=\varnothing \right ]$
6.3. $\left\{\begin{matrix} 5x-8>0\\3x-9>0 \end{matrix}\right.$	$\left [ x>3 \right ]$
6.4. $\left\{\begin{matrix} 2x-3\geq 0\\3x-10\leq 0 \end{matrix}\right.$	$\left [ \cfrac{3}{2}\leq x\leq \cfrac{10}{3} \right ]$
6.5. $\left\{\begin{matrix} 2-3x> 0\\3-2x\geq 0 \end{matrix}\right.$	$\left [ x<\cfrac{2}{3} \right ]$
6.6. $\left\{\begin{matrix} 2x-5 \geq 0\\7-2x> 0 \end{matrix}\right.$	$\left [ \cfrac{5}{2}\leq x<\cfrac{7}{2} \right ]$
6.7. $\left\{\begin{matrix} 3x-4> 0\\5x-8>0 \end{matrix}\right.$	$\left [ x>\cfrac{8}{5} \right ]$
6.8. $\left\{\begin{matrix} 7x-5< 0\\4x+1<0 \end{matrix}\right.$	$\left [ x<-\cfrac{1}{4} \right ]$
6.9. $\left\{\begin{matrix} 3x+4> 0\\4x-5<0 \end{matrix}\right.$	$\left [ -\cfrac{4}{3}<x<\cfrac{5}{4} \right ]$

Per un livello discreto (7)

7.1. $\left\{\begin{matrix} \cfrac{x-2}{3}+x<1\\2x-3<\cfrac{2x+1}{4} \end{matrix}\right.$	$\left [ x<\cfrac{5}{4} \right ]$
7.2. $\left\{\begin{matrix} 3+\cfrac{1-x}{3}>-\cfrac{x+1}{2}\\ \cfrac{1-x}{5}>1 \end{matrix}\right.$	$\left[-23<x<-4\right]$
7.3. $\left\{\begin{matrix} \cfrac{5x+1}{3}>3+\cfrac{x+3}{4}\\ \cfrac{5x-4}{3}-\cfrac{1-2x}{6}>0 \end{matrix}\right.$	$\left [ x>\cfrac{41}{17}\right ]$

Per un buon livello (8)

8.1. $\left\{\begin{matrix} 3x-1>0\\x-3\leqslant 0 \\ 2x+2\geqslant 0 \end{matrix}\right$ .	$\left [ \cfrac{1}{3}<x\leqslant 3 \right ]$
8.2. $\left\{\begin{matrix} 3-4x\leqslant 0\\ 2-x>0\\5x-3\geqslant 0 \end{matrix}\right.$	$\left [ \cfrac{3}{4}\leqslant x<2 \right ]$
8.3. $\left\{\begin{matrix} 5x-1\geqslant 0\\2-3x>0 \\ 4x-3\leqslant 0 \end{matrix}\right.$	$\left [ \cfrac{1}{5}\leqslant x< \cfrac{2}{3} \right ]$
8.4. $\left\{\begin{matrix} 4-5x\leqslant 0\\2x-3<0 \\5-7x>0 \end{matrix}\right.$	$\left[S=\varnothing\right]$
8.5. $\left\{\begin{matrix} x+2>3\\2x-1>x+5 \\ x<2x+4 \end{matrix}\right.$	$\left [ x>6 \right ]$
8.6. $\left\{\begin{matrix} 3\left ( x+3 \right )-2\left ( x-1 \right )>12\\ 3x-2>2\left ( x-1 \right )+3\\x-3\left ( x+2 \right )<2x-2 \end{matrix}\right.$	$\left [ x>3 \right ]$

Verso un ottimo livello (9/10)

9.1. $\left\{\begin{matrix} 3-4x\leqslant 0\\10-13x>0 \\9x-7<0 \\ 5x-4\leqslant 0 \end{matrix}\right.$	$\left [ \cfrac{3}{4}\leqslant x<\frac{10}{13} \right ]$
9.2. $\left\{\begin{matrix} 2x+2\geqslant 3x\\3x-1<4+x \\ 3x+1\geqslant 2x+3\\2-x<0 \\2x-1<x+3 \end{matrix}\right.$	$\left[S=\varnothing\right]$