Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-6}& = &-11 \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6} & = &-11\color{blue}{+6} \\\Leftrightarrow &9x & = &-5\\\Leftrightarrow & \color{red}{9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-6}& = &13 \\\Leftrightarrow & 6x \color{red}{-6}\color{blue}{+6} & = &13\color{blue}{+6} \\\Leftrightarrow &6x & = &19\\\Leftrightarrow & \color{red}{6}x & = &19\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{19}{6} \\\Leftrightarrow & \color{green}{ x = \frac{19}{6} } & & \\ & V = \left\{ \frac{19}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+14}& = &5 \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14} & = &5\color{blue}{-14} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+13}& = &-3 \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13} & = &-3\color{blue}{-13} \\\Leftrightarrow &15x & = &-16\\\Leftrightarrow & \color{red}{15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-16}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-5}& = &13 \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5} & = &13\color{blue}{+5} \\\Leftrightarrow &-15x & = &18\\\Leftrightarrow & \color{red}{-15}x & = &18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+13}& = &-10 \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13} & = &-10\color{blue}{-13} \\\Leftrightarrow &-2x & = &-23\\\Leftrightarrow & \color{red}{-2}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-23}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{23}{2} } & & \\ & V = \left\{ \frac{23}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-2}& = &6 \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2} & = &6\color{blue}{+2} \\\Leftrightarrow &5x & = &8\\\Leftrightarrow & \color{red}{5}x & = &8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-12}& = &-8 \\\Leftrightarrow & -4x \color{red}{-12}\color{blue}{+12} & = &-8\color{blue}{+12} \\\Leftrightarrow &-4x & = &4\\\Leftrightarrow & \color{red}{-4}x & = &4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{4}{-4} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-6}& = &-15 \\\Leftrightarrow & 6x \color{red}{-6}\color{blue}{+6} & = &-15\color{blue}{+6} \\\Leftrightarrow &6x & = &-9\\\Leftrightarrow & \color{red}{6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+2}& = &-7 \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2} & = &-7\color{blue}{-2} \\\Leftrightarrow &3x & = &-9\\\Leftrightarrow & \color{red}{3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-9}{3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-9}& = &5 \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9} & = &5\color{blue}{+9} \\\Leftrightarrow &13x & = &14\\\Leftrightarrow & \color{red}{13}x & = &14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+13}& = &3 \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13} & = &3\color{blue}{-13} \\\Leftrightarrow &-6x & = &-10\\\Leftrightarrow & \color{red}{-6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)