Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-x } & = & -8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &x & = &-20\\\Leftrightarrow & \color{red}{}x & = &-20\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -20 \\\Leftrightarrow & \color{green}{ x = -20 } & & \\ & V = \left\{ -20 \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+9}& = & -10 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9+3x } & = & -10 \color{red}{ -3x }\color{blue}{-9+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -10 \color{blue}{-9} \\\Leftrightarrow &13x & = &-19\\\Leftrightarrow & \color{red}{13}x & = &-19\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-19}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-13}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-x } & = & 5 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 5 \color{blue}{+13} \\\Leftrightarrow &-14x & = &18\\\Leftrightarrow & \color{red}{-14}x & = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+5}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5-5x } & = & -14 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & 7x \color{blue}{-5x } & = & -14 \color{blue}{-5} \\\Leftrightarrow &2x & = &-19\\\Leftrightarrow & \color{red}{2}x & = &-19\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-19}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{2} } & & \\ & V = \left\{ \frac{-19}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-6}& = & -9 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6+4x } & = & -9 \color{red}{ -4x }\color{blue}{+6+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -9 \color{blue}{+6} \\\Leftrightarrow &9x & = &-3\\\Leftrightarrow & \color{red}{9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+14}& = & 10 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14+13x } & = & 10 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &27x & = &-4\\\Leftrightarrow & \color{red}{27}x & = &-4\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-4}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{27} } & & \\ & V = \left\{ \frac{-4}{27} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+2}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2-13x } & = & -2 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -2 \color{blue}{-2} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+9}& = & -2 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9+4x } & = & -2 \color{red}{ -4x }\color{blue}{-9+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &13x & = &-11\\\Leftrightarrow & \color{red}{13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-8}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8-x } & = & 8 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &5x & = &16\\\Leftrightarrow & \color{red}{5}x & = &16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+4}& = & -4 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4+14x } & = & -4 \color{red}{ -14x }\color{blue}{-4+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -4 \color{blue}{-4} \\\Leftrightarrow &17x & = &-8\\\Leftrightarrow & \color{red}{17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-8}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{17} } & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+13}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13-x } & = & -15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &13x & = &-28\\\Leftrightarrow & \color{red}{13}x & = &-28\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-28}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{13} } & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+11}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-x } & = & 10 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &-14x & = &-1\\\Leftrightarrow & \color{red}{-14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)