Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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