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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-12}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12+11x } & = & -10 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &25x & = &2\\\Leftrightarrow & \color{red}{25}x & = &2\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{2}{25} \\\Leftrightarrow & \color{green}{ x = \frac{2}{25} } & & \\ & V = \left\{ \frac{2}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-2}& = & -12 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2+14x } & = & -12 \color{red}{ -14x }\color{blue}{+2+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -12 \color{blue}{+2} \\\Leftrightarrow &19x & = &-10\\\Leftrightarrow & \color{red}{19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12-x } & = & 10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-6}& = & -5 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6+9x } & = & -5 \color{red}{ -9x }\color{blue}{+6+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &19x & = &1\\\Leftrightarrow & \color{red}{19}x & = &1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13-x } & = & 4 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{+13} \\\Leftrightarrow &-3x & = &17\\\Leftrightarrow & \color{red}{-3}x & = &17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{3} } & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-12}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12-5x } & = & 6 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & 9x \color{blue}{-5x } & = & 6 \color{blue}{+12} \\\Leftrightarrow &4x & = &18\\\Leftrightarrow & \color{red}{4}x & = &18\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{18}{4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+6}& = & 4 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-8x } & = & 4 \color{red}{ +8x }\color{blue}{-6-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & 4 \color{blue}{-6} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-10}& = & 10 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10-2x } & = & 10 \color{red}{ +2x }\color{blue}{+10-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & 10 \color{blue}{+10} \\\Leftrightarrow &9x & = &20\\\Leftrightarrow & \color{red}{9}x & = &20\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{20}{9} \\\Leftrightarrow & \color{green}{ x = \frac{20}{9} } & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+4}& = & 5 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4+8x } & = & 5 \color{red}{ -8x }\color{blue}{-4+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &19x & = &1\\\Leftrightarrow & \color{red}{19}x & = &1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+3}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3+13x } & = & 12 \color{red}{ -13x }\color{blue}{-3+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &24x & = &9\\\Leftrightarrow & \color{red}{24}x & = &9\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{9}{24} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+7}& = & 3 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7+4x } & = & 3 \color{red}{ -4x }\color{blue}{-7+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &13x & = &-4\\\Leftrightarrow & \color{red}{13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+10}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-x } & = & 2 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 2 \color{blue}{-10} \\\Leftrightarrow &-10x & = &-8\\\Leftrightarrow & \color{red}{-10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)