Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+14}& = & 11 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14+5x } & = & 11 \color{red}{ -5x }\color{blue}{-14+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 11 \color{blue}{-14} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-11}& = & -15 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-12x } & = & -15 \color{red}{ +12x }\color{blue}{+11-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -15 \color{blue}{+11} \\\Leftrightarrow &-23x & = &-4\\\Leftrightarrow & \color{red}{-23}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-4}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{4}{23} } & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-13}& = & -15 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-13}\color{blue}{+13+4x } & = & -15 \color{red}{ -4x }\color{blue}{+13+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -15 \color{blue}{+13} \\\Leftrightarrow &13x & = &-2\\\Leftrightarrow & \color{red}{13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+5}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5+11x } & = & -8 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &23x & = &-13\\\Leftrightarrow & \color{red}{23}x & = &-13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{23} } & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-8}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-11x } & = & -14 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &-16x & = &-6\\\Leftrightarrow & \color{red}{-16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+7}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7-x } & = & -12 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &-7x & = &-19\\\Leftrightarrow & \color{red}{-7}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+13}& = & -10 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13+8x } & = & -10 \color{red}{ -8x }\color{blue}{-13+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &17x & = &-23\\\Leftrightarrow & \color{red}{17}x & = &-23\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-23}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{17} } & & \\ & V = \left\{ \frac{-23}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+14}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-x } & = & 10 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &-6x & = &-4\\\Leftrightarrow & \color{red}{-6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-7}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7+13x } & = & -11 \color{red}{ -13x }\color{blue}{+7+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -11 \color{blue}{+7} \\\Leftrightarrow &20x & = &-4\\\Leftrightarrow & \color{red}{20}x & = &-4\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-4}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-8}& = & 3 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8+3x } & = & 3 \color{red}{ -3x }\color{blue}{+8+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 3 \color{blue}{+8} \\\Leftrightarrow &13x & = &11\\\Leftrightarrow & \color{red}{13}x & = &11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-2}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-x } & = & -4 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -4 \color{blue}{+2} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-1}& = & 10 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1+8x } & = & 10 \color{red}{ -8x }\color{blue}{+1+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 10 \color{blue}{+1} \\\Leftrightarrow &17x & = &11\\\Leftrightarrow & \color{red}{17}x & = &11\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{11}{17} \\\Leftrightarrow & \color{green}{ x = \frac{11}{17} } & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)