Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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