Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-12}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12+11x } & = & 2 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & -x \color{blue}{+11x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &10x & = &14\\\Leftrightarrow & \color{red}{10}x & = &14\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{14}{10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-1}& = & -8 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1+5x } & = & -8 \color{red}{ -5x }\color{blue}{+1+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & -8 \color{blue}{+1} \\\Leftrightarrow &6x & = &-7\\\Leftrightarrow & \color{red}{6}x & = &-7\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-7}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+8}& = & 10 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8+3x } & = & 10 \color{red}{ -3x }\color{blue}{-8+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &13x & = &2\\\Leftrightarrow & \color{red}{13}x & = &2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+7}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7-x } & = & -8 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -8 \color{blue}{-7} \\\Leftrightarrow &5x & = &-15\\\Leftrightarrow & \color{red}{5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-10}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-x } & = & 15 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &-3x & = &25\\\Leftrightarrow & \color{red}{-3}x & = &25\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{25}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{3} } & & \\ & V = \left\{ \frac{-25}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+5}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5-11x } & = & -12 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & -x \color{blue}{-11x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &-12x & = &-17\\\Leftrightarrow & \color{red}{-12}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-17}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{17}{12} } & & \\ & V = \left\{ \frac{17}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x } & = & 4 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 4 \color{blue}{+13} \\\Leftrightarrow &-8x & = &17\\\Leftrightarrow & \color{red}{-8}x & = &17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{8} } & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-13}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13-13x } & = & 1 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & 1 \color{blue}{+13} \\\Leftrightarrow &-x & = &14\\\Leftrightarrow & \color{red}{-}x & = &14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{14}{-1} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+15}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-x } & = & 13 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 13 \color{blue}{-15} \\\Leftrightarrow &-12x & = &-2\\\Leftrightarrow & \color{red}{-12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+10}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+10}\color{blue}{-10-x } & = & -12 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -12 \color{blue}{-10} \\\Leftrightarrow &-9x & = &-22\\\Leftrightarrow & \color{red}{-9}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-22}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{22}{9} } & & \\ & V = \left\{ \frac{22}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+15}& = & 6 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{+15}\color{blue}{-15-12x } & = & 6 \color{red}{ +12x }\color{blue}{-15-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & 6 \color{blue}{-15} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-10}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10-x } & = & -2 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{+10} \\\Leftrightarrow &-15x & = &8\\\Leftrightarrow & \color{red}{-15}x & = &8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)