Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-1}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-13x } & = & 1 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 1 \color{blue}{+1} \\\Leftrightarrow &-25x & = &2\\\Leftrightarrow & \color{red}{-25}x & = &2\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{2}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{25} } & & \\ & V = \left\{ \frac{-2}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+14}& = & 12 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14+3x } & = & 12 \color{red}{ -3x }\color{blue}{-14+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-14}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14-x } & = & -11 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -11 \color{blue}{+14} \\\Leftrightarrow &13x & = &3\\\Leftrightarrow & \color{red}{13}x & = &3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-7}& = & -12 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7+13x } & = & -12 \color{red}{ -13x }\color{blue}{+7+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -12 \color{blue}{+7} \\\Leftrightarrow &24x & = &-5\\\Leftrightarrow & \color{red}{24}x & = &-5\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-5}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{24} } & & \\ & V = \left\{ \frac{-5}{24} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-14}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14-13x } & = & -12 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -12 \color{blue}{+14} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+2}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-5x } & = & 9 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & 9 \color{blue}{-2} \\\Leftrightarrow &9x & = &7\\\Leftrightarrow & \color{red}{9}x & = &7\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{7}{9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-15}& = & 12 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15+8x } & = & 12 \color{red}{ -8x }\color{blue}{+15+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &17x & = &27\\\Leftrightarrow & \color{red}{17}x & = &27\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{27}{17} \\\Leftrightarrow & \color{green}{ x = \frac{27}{17} } & & \\ & V = \left\{ \frac{27}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-x } & = & -3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+13}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13+11x } & = & -14 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -14 \color{blue}{-13} \\\Leftrightarrow &14x & = &-27\\\Leftrightarrow & \color{red}{14}x & = &-27\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-27}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{14} } & & \\ & V = \left\{ \frac{-27}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-15}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15-x } & = & 9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &x & = &24\\\Leftrightarrow & \color{red}{}x & = &24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 24 \\\Leftrightarrow & \color{green}{ x = 24 } & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-7}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-9x } & = & 12 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &-13x & = &19\\\Leftrightarrow & \color{red}{-13}x & = &19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+11}& = & 11 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-9x } & = & 11 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 11 \color{blue}{-11} \\\Leftrightarrow &-17x & = &0\\\Leftrightarrow & \color{red}{-17}x & = &0\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{0}{-17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)