Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-9}& = &-11 \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9} & = &-11\color{blue}{+9} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+3}& = &9 \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3} & = &9\color{blue}{-3} \\\Leftrightarrow &-x & = &6\\\Leftrightarrow & \color{red}{-}x & = &6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{6}{-1} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-2}& = &11 \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2} & = &11\color{blue}{+2} \\\Leftrightarrow &14x & = &13\\\Leftrightarrow & \color{red}{14}x & = &13\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{13}{14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+12}& = &-13 \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12} & = &-13\color{blue}{-12} \\\Leftrightarrow &11x & = &-25\\\Leftrightarrow & \color{red}{11}x & = &-25\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-25}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{11} } & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-8}& = &12 \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8} & = &12\color{blue}{+8} \\\Leftrightarrow &10x & = &20\\\Leftrightarrow & \color{red}{10}x & = &20\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{20}{10} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+4}& = &-14 \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4} & = &-14\color{blue}{-4} \\\Leftrightarrow &8x & = &-18\\\Leftrightarrow & \color{red}{8}x & = &-18\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-18}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-3}& = &1 \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3} & = &1\color{blue}{+3} \\\Leftrightarrow &-6x & = &4\\\Leftrightarrow & \color{red}{-6}x & = &4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+13}& = &9 \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13} & = &9\color{blue}{-13} \\\Leftrightarrow &9x & = &-4\\\Leftrightarrow & \color{red}{9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-2}& = &8 \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2} & = &8\color{blue}{+2} \\\Leftrightarrow &-4x & = &10\\\Leftrightarrow & \color{red}{-4}x & = &10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+5}& = &-4 \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5} & = &-4\color{blue}{-5} \\\Leftrightarrow &5x & = &-9\\\Leftrightarrow & \color{red}{5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-10}& = &14 \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10} & = &14\color{blue}{+10} \\\Leftrightarrow &x & = &24\\\Leftrightarrow & \color{red}{}x & = &24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 24 \\\Leftrightarrow & \color{green}{ x = 24 } & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+9}& = &-9 \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9} & = &-9\color{blue}{-9} \\\Leftrightarrow &10x & = &-18\\\Leftrightarrow & \color{red}{10}x & = &-18\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-18}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)