Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+6}& = &7 \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6} & = &7\color{blue}{-6} \\\Leftrightarrow &10x & = &1\\\Leftrightarrow & \color{red}{10}x & = &1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+13}& = &7 \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13} & = &7\color{blue}{-13} \\\Leftrightarrow &-13x & = &-6\\\Leftrightarrow & \color{red}{-13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+12}& = &-7 \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12} & = &-7\color{blue}{-12} \\\Leftrightarrow &3x & = &-19\\\Leftrightarrow & \color{red}{3}x & = &-19\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-19}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{3} } & & \\ & V = \left\{ \frac{-19}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-12}& = &-12 \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12} & = &-12\color{blue}{+12} \\\Leftrightarrow &2x & = &0\\\Leftrightarrow & \color{red}{2}x & = &0\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{0}{2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+3}& = &6 \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3} & = &6\color{blue}{-3} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+9}& = &-2 \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9} & = &-2\color{blue}{-9} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+7}& = &15 \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7} & = &15\color{blue}{-7} \\\Leftrightarrow &9x & = &8\\\Leftrightarrow & \color{red}{9}x & = &8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+9}& = &-4 \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9} & = &-4\color{blue}{-9} \\\Leftrightarrow &-13x & = &-13\\\Leftrightarrow & \color{red}{-13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-6}& = &12 \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6} & = &12\color{blue}{+6} \\\Leftrightarrow &-14x & = &18\\\Leftrightarrow & \color{red}{-14}x & = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+13}& = &-2 \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13} & = &-2\color{blue}{-13} \\\Leftrightarrow &-x & = &-15\\\Leftrightarrow & \color{red}{-}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-15}{-1} \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+13}& = &-8 \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13} & = &-8\color{blue}{-13} \\\Leftrightarrow &3x & = &-21\\\Leftrightarrow & \color{red}{3}x & = &-21\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-21}{3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-9}& = &5 \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9} & = &5\color{blue}{+9} \\\Leftrightarrow &-11x & = &14\\\Leftrightarrow & \color{red}{-11}x & = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)