Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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