Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-13}& = & -15 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13+5x } & = & -15 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -15 \color{blue}{+13} \\\Leftrightarrow &8x & = &-2\\\Leftrightarrow & \color{red}{8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+4}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4+11x } & = & -14 \color{red}{ -11x }\color{blue}{-4+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &17x & = &-18\\\Leftrightarrow & \color{red}{17}x & = &-18\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-18}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{17} } & & \\ & V = \left\{ \frac{-18}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4-x } & = & -6 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -6 \color{blue}{+4} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+15}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15-x } & = & -4 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -4 \color{blue}{-15} \\\Leftrightarrow &5x & = &-19\\\Leftrightarrow & \color{red}{5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-19}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-7}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7+2x } & = & 2 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & 13x \color{blue}{+2x } & = & 2 \color{blue}{+7} \\\Leftrightarrow &15x & = &9\\\Leftrightarrow & \color{red}{15}x & = &9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-5}& = & -9 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5-4x } & = & -9 \color{red}{ +4x }\color{blue}{+5-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+5}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5-13x } & = & -1 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &2x & = &-6\\\Leftrightarrow & \color{red}{2}x & = &-6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-6}{2} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-5}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-9x } & = & -9 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &-17x & = &-4\\\Leftrightarrow & \color{red}{-17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+6}& = & 14 \color{red}{ +2x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6-2x } & = & 14 \color{red}{ +2x }\color{blue}{-6-2x } \\\Leftrightarrow & 5x \color{blue}{-2x } & = & 14 \color{blue}{-6} \\\Leftrightarrow &3x & = &8\\\Leftrightarrow & \color{red}{3}x & = &8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-9}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9-x } & = & 5 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 5 \color{blue}{+9} \\\Leftrightarrow &13x & = &14\\\Leftrightarrow & \color{red}{13}x & = &14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-4}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-x } & = & -5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+5}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5-7x } & = & 11 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &8x & = &6\\\Leftrightarrow & \color{red}{8}x & = &6\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{6}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)