Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(2x-14=13+x\)
2. \(2x+10=12+11x\)
3. \(13x+4=1+11x\)
4. \(15x+12=-2+11x\)
5. \(11x+3=-15+14x\)
6. \(-12x-10=11+13x\)
7. \(12x+5=-4-7x\)
8. \(-9x-14=10+x\)
9. \(10x+7=-7-3x\)
10. \(13x-14=-7+x\)
11. \(-6x+2=9+x\)
12. \(9x+10=14-13x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-14}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-x } & = & 13 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 13 \color{blue}{+14} \\\Leftrightarrow &x & = &27\\\Leftrightarrow & \color{red}{}x & = &27\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 27 \\\Leftrightarrow & \color{green}{ x = 27 } & & \\ & V = \left\{ 27 \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+10}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-11x } & = & 12 \color{red}{ +11x }\color{blue}{-10-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+4}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4-11x } & = & 1 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 13x \color{blue}{-11x } & = & 1 \color{blue}{-4} \\\Leftrightarrow &2x & = &-3\\\Leftrightarrow & \color{red}{2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+12}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+12}\color{blue}{-12-11x } & = & -2 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -2 \color{blue}{-12} \\\Leftrightarrow &4x & = &-14\\\Leftrightarrow & \color{red}{4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-14}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+3}& = & -15 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3-14x } & = & -15 \color{red}{ +14x }\color{blue}{-3-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &-3x & = &-18\\\Leftrightarrow & \color{red}{-3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-18}{-3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-10}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-13x } & = & 11 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &-25x & = &21\\\Leftrightarrow & \color{red}{-25}x & = &21\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{21}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{25} } & & \\ & V = \left\{ \frac{-21}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+5}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5+7x } & = & -4 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -4 \color{blue}{-5} \\\Leftrightarrow &19x & = &-9\\\Leftrightarrow & \color{red}{19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-14}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-x } & = & 10 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 10 \color{blue}{+14} \\\Leftrightarrow &-10x & = &24\\\Leftrightarrow & \color{red}{-10}x & = &24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+7}& = & -7 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7+3x } & = & -7 \color{red}{ -3x }\color{blue}{-7+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &13x & = &-14\\\Leftrightarrow & \color{red}{13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14-x } & = & -7 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &12x & = &7\\\Leftrightarrow & \color{red}{12}x & = &7\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{7}{12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+2}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-x } & = & 9 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 9 \color{blue}{-2} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+10}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10+13x } & = & 14 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 14 \color{blue}{-10} \\\Leftrightarrow &22x & = &4\\\Leftrightarrow & \color{red}{22}x & = &4\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{4}{22} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)