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Hitova: 3116

Zadatak 11. Riješi nejednadžbu

\[ \dfrac{3x+1}{x-3}\leq -3 \]

Rješenje: Kao prvo napraviti nlu na desnoj strani

\[ \dfrac{3x+1}{x-3}-3\leq 0 \]

\[ \dfrac{6x-8}{x-3}\leq 0 \]

a)    \(6x-8\leq 0\)        b)    \(6x-8\geq 0\)
\(x-3>0\) \( x-3<0\)
                 
\(x\leq \frac{4}{3}\)  \(x\geq\dfrac{4}{3}\)
\(x>3\)  \(x<3\)
                 
 \(R_a: x\in \emptyset\)  \(R_b: x\in \left[\frac{4}{3},3\right>\)

Rješenje zadatka je unija rješenja sustava pod a) i b):

\[ R=R_a\cup R_b=\left[ \dfrac{4}{3},3\right>\]

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Hitova: 9599

 \(\large{\mathbf{1.}\mspace{3mu}Riješi\:\:nejednadžbe:}\)

\(\mspace{50mu}\large{\mathbf{1)}\mspace{15mu}7-4x<0;\mspace{30mu}\mathbf{2)}\mspace{15mu}3x+1\geq x+7;}\)

\(\mspace{50mu}\large{\mathbf{3)}\mspace{15mu}\dfrac{1}{5}x+6<x;\mspace{30mu}\mathbf{4)}\mspace{15mu}x+11\leq 3x-5;}\)

\(\mspace{50mu}\large{\mathbf{5)}\mspace{15mu}3-9x<0;\mspace{30mu}\mathbf{6)}\mspace{15mu}-5-2x>0;}\)

\(\mspace{50mu}\large{\mathbf{7)}\mspace{15mu}-3x+1\leq 2;\mspace{30mu}\mathbf{8)}\mspace{15mu}2x+5\geq -x-7;}\)