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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+12}& = & -1 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12+5x } & = & -1 \color{red}{ -5x }\color{blue}{-12+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -1 \color{blue}{-12} \\\Leftrightarrow &8x & = &-13\\\Leftrightarrow & \color{red}{8}x & = &-13\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-13}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-4}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-4}\color{blue}{+4-x } & = & 14 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 14 \color{blue}{+4} \\\Leftrightarrow &-15x & = &18\\\Leftrightarrow & \color{red}{-15}x & = &18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+12}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12-5x } & = & -13 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & 9x \color{blue}{-5x } & = & -13 \color{blue}{-12} \\\Leftrightarrow &4x & = &-25\\\Leftrightarrow & \color{red}{4}x & = &-25\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-25}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{4} } & & \\ & V = \left\{ \frac{-25}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+12}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+12}\color{blue}{-12-x } & = & 1 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 1 \color{blue}{-12} \\\Leftrightarrow &-13x & = &-11\\\Leftrightarrow & \color{red}{-13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-5}& = & -14 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5-4x } & = & -14 \color{red}{ +4x }\color{blue}{+5-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &-19x & = &-9\\\Leftrightarrow & \color{red}{-19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{9}{19} } & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-10}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-13x } & = & 1 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 1 \color{blue}{+10} \\\Leftrightarrow &-28x & = &11\\\Leftrightarrow & \color{red}{-28}x & = &11\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{11}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{28} } & & \\ & V = \left\{ \frac{-11}{28} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-5}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-13x } & = & 14 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &-18x & = &19\\\Leftrightarrow & \color{red}{-18}x & = &19\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{19}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{18} } & & \\ & V = \left\{ \frac{-19}{18} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+6}& = & 11 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6+14x } & = & 11 \color{red}{ -14x }\color{blue}{-6+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 11 \color{blue}{-6} \\\Leftrightarrow &19x & = &5\\\Leftrightarrow & \color{red}{19}x & = &5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+13}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-3x } & = & 1 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 1 \color{blue}{-13} \\\Leftrightarrow &-8x & = &-12\\\Leftrightarrow & \color{red}{-8}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+11}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-x } & = & 10 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-6}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6+7x } & = & 15 \color{red}{ -7x }\color{blue}{+6+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &11x & = &21\\\Leftrightarrow & \color{red}{11}x & = &21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-5}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-7x } & = & -15 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -15 \color{blue}{+5} \\\Leftrightarrow &-5x & = &-10\\\Leftrightarrow & \color{red}{-5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)