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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-10}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10-x } & = & -3 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -3 \color{blue}{+10} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-8}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-9x } & = & -8 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -8 \color{blue}{+8} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-2}& = & 5 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2+3x } & = & 5 \color{red}{ -3x }\color{blue}{+2+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 5 \color{blue}{+2} \\\Leftrightarrow &10x & = &7\\\Leftrightarrow & \color{red}{10}x & = &7\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{7}{10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+3}& = & 4 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3+4x } & = & 4 \color{red}{ -4x }\color{blue}{-3+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+15}& = & -3 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-8x } & = & -3 \color{red}{ +8x }\color{blue}{-15-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & -3 \color{blue}{-15} \\\Leftrightarrow &-21x & = &-18\\\Leftrightarrow & \color{red}{-21}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-18}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-11}& = & 2 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11+9x } & = & 2 \color{red}{ -9x }\color{blue}{+11+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 2 \color{blue}{+11} \\\Leftrightarrow &14x & = &13\\\Leftrightarrow & \color{red}{14}x & = &13\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{13}{14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+10}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-13x } & = & -1 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &-18x & = &-11\\\Leftrightarrow & \color{red}{-18}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-11}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{11}{18} } & & \\ & V = \left\{ \frac{11}{18} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-14}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-x } & = & -3 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &-14x & = &11\\\Leftrightarrow & \color{red}{-14}x & = &11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-11}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-x } & = & -4 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &-4x & = &7\\\Leftrightarrow & \color{red}{-4}x & = &7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+11}& = & 9 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11-6x } & = & 9 \color{red}{ +6x }\color{blue}{-11-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & 9 \color{blue}{-11} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-8}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-11x } & = & 4 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &-18x & = &12\\\Leftrightarrow & \color{red}{-18}x & = &12\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{12}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+15}& = & -14 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15+15x } & = & -14 \color{red}{ -15x }\color{blue}{-15+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &28x & = &-29\\\Leftrightarrow & \color{red}{28}x & = &-29\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{-29}{28} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{28} } & & \\ & V = \left\{ \frac{-29}{28} \right\} & \\\end{align}\)