Lineární nerovnice

1. V množině přirozených čísel řešte nerovnice

$$(a)\ 5x-2<6 x+5$$ $$(b)\ 10x-2<6 x+5$$

$$(c)\ 0,1x-0,2<24,1-5,3x$$ $$(d)\ 18,3-7,2x>6,1+1,35x$$

$$(a)\ x\in\mathbb N$$ $$(b)\ x\in\{1\}$$

$$(c)\ x\in\{1,2,3,4\}$$ $$(d)\ x\in\{1\}$$

2. V množině reálných čísel řešte nerovnice

$$(a)\ \frac{3x}{2}+4>3$$ $$(b)\ \frac{2x}{3}+8>\frac{3x}{5}$$ $$(c)\ x+1>\frac{3x}{4}-5$$

$$(d)\ 3x-\frac{1}{4}<\frac{5x+1}{6}$$ $$(e)\ \frac{4x+3}{4}-\frac{3x-1}{6}\leq\frac{1}{5}$$ $$(f)\ 12+x<\frac{x}{2}-\frac{2x-3}{4}-\frac{1}{2}$$

$$(g)\ \frac{2x-4}{3}-\frac{2-x}{4}>\frac{x}{6}-\frac{x+6}{5}$$ $$(h)\ \frac{2x+3}{5}-\frac{2x-4}{6}>\frac{9x-6}{14}$$ $$(i)\ \frac{3x-4}{2}<\frac{5x-1}{3}+3-2x$$

$$(j)\ \frac{2(2x-3)-3x-1}{4}\leq 0$$ $$(k)\ \frac{2(2x+1)}{5}<\frac{x+1}{2}+2$$ $$(l)\ 4-\frac{7-3x}{5}\geq 3-\frac{3-7x}{10}-\frac{x+1}{2}$$

$$(a)\ x\in\left(-\frac{2}{3},\infty\right)$$ $$(b)\ x\in\left ( -120,\infty \right )$$ $$(c)\ x\in\left ( -24,\infty \right )$$

$$(d)\ x\in\left ( -\infty,\frac{5}{26} \right )$$ $$(e)\ x\in\left ( -\infty,-\frac{43}{30} \right \rangle$$ $$(f)\ x\in\left ( -\infty,-\frac{47}{12} \right )$$

$$(g)\ x\in\left ( \frac{2}{3},\infty \right )$$ $$(h)\ x\in\left ( -\infty,\frac{356}{121} \right )$$ $$(i)\ x\in\left ( -\infty,\frac{28}{11} \right )$$

$$(j)\ x\in\left ( -\infty, 7 \right \rangle$$ $$(k)\ x\in\left ( -\infty, 3 \right )$$ $$(l)\ x\in\left \langle -1,\infty \right )$$

$$(a)\ 5x-2<6 x+5$$	$$(b)\ 10x-2<6 x+5$$
$$(c)\ 0,1x-0,2<24,1-5,3x$$	$$(d)\ 18,3-7,2x>6,1+1,35x$$

$$(a)\ x\in\mathbb N$$	$$(b)\ x\in\{1\}$$
$$(c)\ x\in\{1,2,3,4\}$$	$$(d)\ x\in\{1\}$$

$$(a)\ \frac{3x}{2}+4>3$$	$$(b)\ \frac{2x}{3}+8>\frac{3x}{5}$$	$$(c)\ x+1>\frac{3x}{4}-5$$
$$(d)\ 3x-\frac{1}{4}<\frac{5x+1}{6}$$	$$(e)\ \frac{4x+3}{4}-\frac{3x-1}{6}\leq\frac{1}{5}$$	$$(f)\ 12+x<\frac{x}{2}-\frac{2x-3}{4}-\frac{1}{2}$$
$$(g)\ \frac{2x-4}{3}-\frac{2-x}{4}>\frac{x}{6}-\frac{x+6}{5}$$	$$(h)\ \frac{2x+3}{5}-\frac{2x-4}{6}>\frac{9x-6}{14}$$	$$(i)\ \frac{3x-4}{2}<\frac{5x-1}{3}+3-2x$$
$$(j)\ \frac{2(2x-3)-3x-1}{4}\leq 0$$	$$(k)\ \frac{2(2x+1)}{5}<\frac{x+1}{2}+2$$	$$(l)\ 4-\frac{7-3x}{5}\geq 3-\frac{3-7x}{10}-\frac{x+1}{2}$$

$$(a)\ x\in\left(-\frac{2}{3},\infty\right)$$	$$(b)\ x\in\left ( -120,\infty \right )$$	$$(c)\ x\in\left ( -24,\infty \right )$$
$$(d)\ x\in\left ( -\infty,\frac{5}{26} \right )$$	$$(e)\ x\in\left ( -\infty,-\frac{43}{30} \right \rangle$$	$$(f)\ x\in\left ( -\infty,-\frac{47}{12} \right )$$
$$(g)\ x\in\left ( \frac{2}{3},\infty \right )$$	$$(h)\ x\in\left ( -\infty,\frac{356}{121} \right )$$	$$(i)\ x\in\left ( -\infty,\frac{28}{11} \right )$$
$$(j)\ x\in\left ( -\infty, 7 \right \rangle$$	$$(k)\ x\in\left ( -\infty, 3 \right )$$	$$(l)\ x\in\left \langle -1,\infty \right )$$