Решени задаци.
Текст задатака објашњених у видео лекцији:
Пр.1) Решити следеће једначине:
а) $\frac{x}{3} - \frac{1}{2} = \frac{x}{4} + \frac{1}{2}$
б) $x - \frac{{2x - 5}}{5} = 4$
в) $\frac{{2x}}{3} - \frac{{x - 3}}{6} - 0,5 = x$
г) $\frac{{3\left( {x - 1} \right)}}{2} + \frac{{x - 4}}{3} = 12 - \frac{{x + 1}}{2}$ д) $\frac{{2x + 3}}{3} - \frac{{5x - 14}}{{12}} = \frac{{x + 1}}{4} - 3$ Пр.1)
| а) |
$\frac{x}{3} - \frac{1}{2} = \frac{x}{4} + \frac{1}{2}$ |
б) |
$x - \frac{{2x - 5}}{5} = 4$ |
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$\frac{x}{3} - \frac{1}{2} = \frac{x}{4} + \frac{1}{2}\left| { \cdot 12} \right.$ |
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$x - \frac{{2x - 5}}{5} = 4\left| { \cdot 5} \right.$ |
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$12 \cdot \frac{x}{3} - 12 \cdot \frac{1}{2} = 12 \cdot \frac{x}{4} + 12 \cdot \frac{1}{2}$ |
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$x \cdot 5 - \frac{{2x - 5}}{5} \cdot 5 = 4 \cdot 5$ |
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$4x - 6 = 3x + 6$ |
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$5x - \left( {2x - 5} \right) = 20$ |
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$4x - 3x = 6 + 6$ |
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$5x - 2x + 5 = 20$ |
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$x = 12$ |
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$5x - 2x = 20 - 5$ |
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$3x = 15$ |
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$x = 5$ |
| в) |
$\frac{{2x}}{3} - \frac{{x - 3}}{6} - 0,5 = x$ |
г) |
$\frac{{3\left( {x - 1} \right)}}{2} + \frac{{x - 4}}{3} = 12 - \frac{{x + 1}}{2}$ |
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$\frac{{2x}}{3} - \frac{{x - 3}}{6} - 0,5 = x\left| { \cdot 6} \right.$ |
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$\frac{{3\left( {x - 1} \right)}}{2} + \frac{{x - 4}}{3} = 12 - \frac{{x + 1}}{2}\left| { \cdot 6} \right.$ |
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$\frac{{2x}}{3} \cdot 6 - \frac{{x - 3}}{6} \cdot 6 - 0,5 \cdot 6 = x \cdot 6$ |
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$\frac{{3\left( {x - 1} \right)}}{2} \cdot 6 + \frac{{x - 4}}{3} \cdot 6 = 12 \cdot 6 - \frac{{x + 1}}{2} \cdot 6$ |
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$4x - \left( {x - 3} \right) - 3 = 6x$ |
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$3 \cdot 3 \cdot \left( {x - 1} \right) + 2 \cdot \left( {x - 4} \right) = 72 - 3 \cdot \left( {x + 1} \right)$ |
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$4x - x + 3 - 3 = 6x$ |
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$9x - 9 + 2x - 8 = 72 - 3x - 3$ |
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$4x - x - 6x = 0$ |
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$11x - 17 = 69 - 3x$ |
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$ - 3x = 0$ |
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$11x + 3x = 69 + 17$ |
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$x = \frac{0}{{ - 3}}$ |
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$14x = 86$ |
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$x = 0$ |
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$x = \frac{{86}}{{14}}$ |
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$x = 6\frac{1}{7}$ |
д)
$\frac{{2x + 3}}{3} - \frac{{5x - 14}}{{12}} = \frac{{x + 1}}{4} - 3$
$ \frac{{2x + 3}}{3} - \frac{{5x - 14}}{{12}} = \frac{{x + 1}}{4} - 3\left| { \cdot 12} \right. $
$\frac{{2x + 3}}{3} \cdot 12 - \frac{{5x - 14}}{{12}} \cdot 12 = \frac{{x + 1}}{4} \cdot 12 - 3 \cdot 12 $
$4 \cdot \left( {2x + 3} \right) - \left( {5x - 14} \right) = 3 \cdot \left( {x + 1} \right) - 36 $
$8x + 12 - 5x + 14 = 3x + 3 - 36 $
$3x + 26 = 3x - 33 $
$0x = - 59 $
$x \in \emptyset $