Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-8}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8-5x } & = & -1 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -1 \color{blue}{+8} \\\Leftrightarrow &7x & = &7\\\Leftrightarrow & \color{red}{7}x & = &7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{7}{7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-14}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-x } & = & 3 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &-10x & = &17\\\Leftrightarrow & \color{red}{-10}x & = &17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{10} } & & \\ & V = \left\{ \frac{-17}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+13}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13-x } & = & -12 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -12 \color{blue}{-13} \\\Leftrightarrow &-16x & = &-25\\\Leftrightarrow & \color{red}{-16}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-25}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{25}{16} } & & \\ & V = \left\{ \frac{25}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-10}& = & 10 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10+7x } & = & 10 \color{red}{ -7x }\color{blue}{+10+7x } \\\Leftrightarrow & -x \color{blue}{+7x } & = & 10 \color{blue}{+10} \\\Leftrightarrow &6x & = &20\\\Leftrightarrow & \color{red}{6}x & = &20\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{20}{6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+1}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-13x } & = & 2 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 2 \color{blue}{-1} \\\Leftrightarrow &-28x & = &1\\\Leftrightarrow & \color{red}{-28}x & = &1\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{1}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{28} } & & \\ & V = \left\{ \frac{-1}{28} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+8}& = & -14 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8-10x } & = & -14 \color{red}{ +10x }\color{blue}{-8-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & -14 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-22\\\Leftrightarrow & \color{red}{-3}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-22}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-3}& = & 9 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3+7x } & = & 9 \color{red}{ -7x }\color{blue}{+3+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 9 \color{blue}{+3} \\\Leftrightarrow &15x & = &12\\\Leftrightarrow & \color{red}{15}x & = &12\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{12}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-12}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12-x } & = & 2 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &-11x & = &14\\\Leftrightarrow & \color{red}{-11}x & = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+2}& = & -1 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2+2x } & = & -1 \color{red}{ -2x }\color{blue}{-2+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & -1 \color{blue}{-2} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-14}\color{blue}{+14-x } & = & -8 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -8 \color{blue}{+14} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-8}& = & 6 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8-12x } & = & 6 \color{red}{ +12x }\color{blue}{+8-12x } \\\Leftrightarrow & 13x \color{blue}{-12x } & = & 6 \color{blue}{+8} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{-6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6-x } & = & 3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 3 \color{blue}{+6} \\\Leftrightarrow &13x & = &9\\\Leftrightarrow & \color{red}{13}x & = &9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)