Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-14}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14-5x } & = & -1 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &-17x & = &13\\\Leftrightarrow & \color{red}{-17}x & = &13\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{13}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{17} } & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14-x } & = & 5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 5 \color{blue}{+14} \\\Leftrightarrow &-3x & = &19\\\Leftrightarrow & \color{red}{-3}x & = &19\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{19}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{3} } & & \\ & V = \left\{ \frac{-19}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-10}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-11x } & = & -10 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & -10 \color{blue}{+10} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+10}& = & 7 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10+3x } & = & 7 \color{red}{ -3x }\color{blue}{-10+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-9}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9-13x } & = & -9 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+8}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-5x } & = & 14 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-7x & = &6\\\Leftrightarrow & \color{red}{-7}x & = &6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+9}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-3x } & = & -15 \color{red}{ +3x }\color{blue}{-9-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &-11x & = &-24\\\Leftrightarrow & \color{red}{-11}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-24}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{24}{11} } & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+11}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-7x } & = & -8 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-19\\\Leftrightarrow & \color{red}{-13}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{19}{13} } & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+3}& = & 10 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3+13x } & = & 10 \color{red}{ -13x }\color{blue}{-3+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 10 \color{blue}{-3} \\\Leftrightarrow &22x & = &7\\\Leftrightarrow & \color{red}{22}x & = &7\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{7}{22} \\\Leftrightarrow & \color{green}{ x = \frac{7}{22} } & & \\ & V = \left\{ \frac{7}{22} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-12}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12-13x } & = & 15 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & 15 \color{blue}{+12} \\\Leftrightarrow &-11x & = &27\\\Leftrightarrow & \color{red}{-11}x & = &27\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{27}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{11} } & & \\ & V = \left\{ \frac{-27}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+8}& = & 1 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8+7x } & = & 1 \color{red}{ -7x }\color{blue}{-8+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &15x & = &-7\\\Leftrightarrow & \color{red}{15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-10}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10+13x } & = & 3 \color{red}{ -13x }\color{blue}{+10+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 3 \color{blue}{+10} \\\Leftrightarrow &20x & = &13\\\Leftrightarrow & \color{red}{20}x & = &13\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{13}{20} \\\Leftrightarrow & \color{green}{ x = \frac{13}{20} } & & \\ & V = \left\{ \frac{13}{20} \right\} & \\\end{align}\)