Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-10}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-7x } & = & -4 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -4 \color{blue}{+10} \\\Leftrightarrow &-20x & = &6\\\Leftrightarrow & \color{red}{-20}x & = &6\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{6}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+14}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-x } & = & 13 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-14}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14-5x } & = & -1 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &-7x & = &13\\\Leftrightarrow & \color{red}{-7}x & = &13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-2}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2-x } & = & -9 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -9 \color{blue}{+2} \\\Leftrightarrow &13x & = &-7\\\Leftrightarrow & \color{red}{13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-9}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-x } & = & 4 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15-x } & = & -14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &13x & = &-29\\\Leftrightarrow & \color{red}{13}x & = &-29\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-29}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{13} } & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+13}& = & 5 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13+2x } & = & 5 \color{red}{ -2x }\color{blue}{-13+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 5 \color{blue}{-13} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-13}& = & -1 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13+11x } & = & -1 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -1 \color{blue}{+13} \\\Leftrightarrow &14x & = &12\\\Leftrightarrow & \color{red}{14}x & = &12\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{12}{14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+14}& = & -1 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14+3x } & = & -1 \color{red}{ -3x }\color{blue}{-14+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &7x & = &-15\\\Leftrightarrow & \color{red}{7}x & = &-15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-8}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8-5x } & = & -8 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -8 \color{blue}{+8} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+15}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15+11x } & = & -7 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &15x & = &-22\\\Leftrightarrow & \color{red}{15}x & = &-22\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-22}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{15} } & & \\ & V = \left\{ \frac{-22}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+3}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-7x } & = & 15 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &-20x & = &12\\\Leftrightarrow & \color{red}{-20}x & = &12\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{12}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)