Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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