Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+6}& = &-6 \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6} & = &-6\color{blue}{-6} \\\Leftrightarrow &10x & = &-12\\\Leftrightarrow & \color{red}{10}x & = &-12\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-12}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-3}& = &-3 \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3} & = &-3\color{blue}{+3} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-9}& = &7 \\\Leftrightarrow & 2x \color{red}{-9}\color{blue}{+9} & = &7\color{blue}{+9} \\\Leftrightarrow &2x & = &16\\\Leftrightarrow & \color{red}{2}x & = &16\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{16}{2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-13}& = &6 \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13} & = &6\color{blue}{+13} \\\Leftrightarrow &-8x & = &19\\\Leftrightarrow & \color{red}{-8}x & = &19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+2}& = &-13 \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2} & = &-13\color{blue}{-2} \\\Leftrightarrow &9x & = &-15\\\Leftrightarrow & \color{red}{9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-15}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-12}& = &14 \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12} & = &14\color{blue}{+12} \\\Leftrightarrow &-3x & = &26\\\Leftrightarrow & \color{red}{-3}x & = &26\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{26}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{3} } & & \\ & V = \left\{ \frac{-26}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+12}& = &-13 \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12} & = &-13\color{blue}{-12} \\\Leftrightarrow &-13x & = &-25\\\Leftrightarrow & \color{red}{-13}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-25}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{25}{13} } & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+4}& = &1 \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4} & = &1\color{blue}{-4} \\\Leftrightarrow &-2x & = &-3\\\Leftrightarrow & \color{red}{-2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-3}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-11}& = &-7 \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11} & = &-7\color{blue}{+11} \\\Leftrightarrow &10x & = &4\\\Leftrightarrow & \color{red}{10}x & = &4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-1}& = &-4 \\\Leftrightarrow & 11x \color{red}{-1}\color{blue}{+1} & = &-4\color{blue}{+1} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-13}& = &-12 \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13} & = &-12\color{blue}{+13} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-7}& = &2 \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7} & = &2\color{blue}{+7} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)