Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-1}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-x } & = & 11 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &-12x & = &12\\\Leftrightarrow & \color{red}{-12}x & = &12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{12}{-12} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-13}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13-x } & = & -9 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -9 \color{blue}{+13} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+13}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13-x } & = & 8 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 8 \color{blue}{-13} \\\Leftrightarrow &5x & = &-5\\\Leftrightarrow & \color{red}{5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-1}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-13x } & = & 5 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 5 \color{blue}{+1} \\\Leftrightarrow &-25x & = &6\\\Leftrightarrow & \color{red}{-25}x & = &6\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{6}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{25} } & & \\ & V = \left\{ \frac{-6}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+3}& = & 5 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3+3x } & = & 5 \color{red}{ -3x }\color{blue}{-3+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &13x & = &2\\\Leftrightarrow & \color{red}{13}x & = &2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+4}& = & 12 \color{red}{ +4x } \\\Leftrightarrow & -11x \color{red}{+4}\color{blue}{-4-4x } & = & 12 \color{red}{ +4x }\color{blue}{-4-4x } \\\Leftrightarrow & -11x \color{blue}{-4x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &-15x & = &8\\\Leftrightarrow & \color{red}{-15}x & = &8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+10}& = & -3 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10-4x } & = & -3 \color{red}{ +4x }\color{blue}{-10-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &9x & = &-13\\\Leftrightarrow & \color{red}{9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-13}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+6}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6+11x } & = & 7 \color{red}{ -11x }\color{blue}{-6+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &14x & = &1\\\Leftrightarrow & \color{red}{14}x & = &1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-1}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1+5x } & = & 2 \color{red}{ -5x }\color{blue}{+1+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &6x & = &3\\\Leftrightarrow & \color{red}{6}x & = &3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-15}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-5x } & = & 1 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 1 \color{blue}{+15} \\\Leftrightarrow &-14x & = &16\\\Leftrightarrow & \color{red}{-14}x & = &16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+14}& = & -5 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14+11x } & = & -5 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & -5 \color{blue}{-14} \\\Leftrightarrow &20x & = &-19\\\Leftrightarrow & \color{red}{20}x & = &-19\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-19}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{20} } & & \\ & V = \left\{ \frac{-19}{20} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+5}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-3x } & = & 5 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &-17x & = &0\\\Leftrightarrow & \color{red}{-17}x & = &0\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{0}{-17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)