Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+13}& = &-5 \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13} & = &-5\color{blue}{-13} \\\Leftrightarrow &5x & = &-18\\\Leftrightarrow & \color{red}{5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+8}& = &5 \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8} & = &5\color{blue}{-8} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-11}& = &3 \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11} & = &3\color{blue}{+11} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-12}& = &-7 \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12} & = &-7\color{blue}{+12} \\\Leftrightarrow &5x & = &5\\\Leftrightarrow & \color{red}{5}x & = &5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{5}{5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-14}& = &8 \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14} & = &8\color{blue}{+14} \\\Leftrightarrow &2x & = &22\\\Leftrightarrow & \color{red}{2}x & = &22\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{22}{2} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+4}& = &-13 \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4} & = &-13\color{blue}{-4} \\\Leftrightarrow &-x & = &-17\\\Leftrightarrow & \color{red}{-}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-17}{-1} \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-13}& = &14 \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13} & = &14\color{blue}{+13} \\\Leftrightarrow &-11x & = &27\\\Leftrightarrow & \color{red}{-11}x & = &27\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{27}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{11} } & & \\ & V = \left\{ \frac{-27}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-6}& = &3 \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6} & = &3\color{blue}{+6} \\\Leftrightarrow &-10x & = &9\\\Leftrightarrow & \color{red}{-10}x & = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-11}& = &-9 \\\Leftrightarrow & -13x \color{red}{-11}\color{blue}{+11} & = &-9\color{blue}{+11} \\\Leftrightarrow &-13x & = &2\\\Leftrightarrow & \color{red}{-13}x & = &2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-10}& = &-9 \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10} & = &-9\color{blue}{+10} \\\Leftrightarrow &-12x & = &1\\\Leftrightarrow & \color{red}{-12}x & = &1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-13}& = &13 \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13} & = &13\color{blue}{+13} \\\Leftrightarrow &-9x & = &26\\\Leftrightarrow & \color{red}{-9}x & = &26\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{26}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{9} } & & \\ & V = \left\{ \frac{-26}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-11}& = &6 \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11} & = &6\color{blue}{+11} \\\Leftrightarrow &-9x & = &17\\\Leftrightarrow & \color{red}{-9}x & = &17\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{17}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{9} } & & \\ & V = \left\{ \frac{-17}{9} \right\} & \\\end{align}\)