Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+13}& = &5 \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13} & = &5\color{blue}{-13} \\\Leftrightarrow &6x & = &-8\\\Leftrightarrow & \color{red}{6}x & = &-8\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-8}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-8}& = &-5 \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8} & = &-5\color{blue}{+8} \\\Leftrightarrow &-8x & = &3\\\Leftrightarrow & \color{red}{-8}x & = &3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-10}& = &-14 \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10} & = &-14\color{blue}{+10} \\\Leftrightarrow &14x & = &-4\\\Leftrightarrow & \color{red}{14}x & = &-4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-15}& = &6 \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15} & = &6\color{blue}{+15} \\\Leftrightarrow &9x & = &21\\\Leftrightarrow & \color{red}{9}x & = &21\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{21}{9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-5}& = &-12 \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5} & = &-12\color{blue}{+5} \\\Leftrightarrow &10x & = &-7\\\Leftrightarrow & \color{red}{10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-7}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-6}& = &13 \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6} & = &13\color{blue}{+6} \\\Leftrightarrow &-5x & = &19\\\Leftrightarrow & \color{red}{-5}x & = &19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+2}& = &9 \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2} & = &9\color{blue}{-2} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+3}& = &8 \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3} & = &8\color{blue}{-3} \\\Leftrightarrow &-9x & = &5\\\Leftrightarrow & \color{red}{-9}x & = &5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-12}& = &11 \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12} & = &11\color{blue}{+12} \\\Leftrightarrow &-11x & = &23\\\Leftrightarrow & \color{red}{-11}x & = &23\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{23}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{11} } & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+8}& = &8 \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8} & = &8\color{blue}{-8} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-12}& = &13 \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12} & = &13\color{blue}{+12} \\\Leftrightarrow &-3x & = &25\\\Leftrightarrow & \color{red}{-3}x & = &25\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{25}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{3} } & & \\ & V = \left\{ \frac{-25}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+7}& = &-6 \\\Leftrightarrow & -3x \color{red}{+7}\color{blue}{-7} & = &-6\color{blue}{-7} \\\Leftrightarrow &-3x & = &-13\\\Leftrightarrow & \color{red}{-3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)