Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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