Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-11}& = &8 \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11} & = &8\color{blue}{+11} \\\Leftrightarrow &10x & = &19\\\Leftrightarrow & \color{red}{10}x & = &19\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{19}{10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-11}& = &-5 \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11} & = &-5\color{blue}{+11} \\\Leftrightarrow &10x & = &6\\\Leftrightarrow & \color{red}{10}x & = &6\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{6}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-9}& = &-4 \\\Leftrightarrow & 6x \color{red}{-9}\color{blue}{+9} & = &-4\color{blue}{+9} \\\Leftrightarrow &6x & = &5\\\Leftrightarrow & \color{red}{6}x & = &5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-10}& = &15 \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10} & = &15\color{blue}{+10} \\\Leftrightarrow &-6x & = &25\\\Leftrightarrow & \color{red}{-6}x & = &25\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{25}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{6} } & & \\ & V = \left\{ \frac{-25}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+13}& = &4 \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13} & = &4\color{blue}{-13} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+15}& = &-13 \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15} & = &-13\color{blue}{-15} \\\Leftrightarrow &5x & = &-28\\\Leftrightarrow & \color{red}{5}x & = &-28\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-28}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{5} } & & \\ & V = \left\{ \frac{-28}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-11}& = &-1 \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11} & = &-1\color{blue}{+11} \\\Leftrightarrow &14x & = &10\\\Leftrightarrow & \color{red}{14}x & = &10\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{10}{14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+14}& = &11 \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14} & = &11\color{blue}{-14} \\\Leftrightarrow &-7x & = &-3\\\Leftrightarrow & \color{red}{-7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-1}& = &7 \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1} & = &7\color{blue}{+1} \\\Leftrightarrow &-13x & = &8\\\Leftrightarrow & \color{red}{-13}x & = &8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-14}& = &9 \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14} & = &9\color{blue}{+14} \\\Leftrightarrow &8x & = &23\\\Leftrightarrow & \color{red}{8}x & = &23\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{23}{8} \\\Leftrightarrow & \color{green}{ x = \frac{23}{8} } & & \\ & V = \left\{ \frac{23}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+13}& = &-6 \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13} & = &-6\color{blue}{-13} \\\Leftrightarrow &-15x & = &-19\\\Leftrightarrow & \color{red}{-15}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{19}{15} } & & \\ & V = \left\{ \frac{19}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+5}& = &11 \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5} & = &11\color{blue}{-5} \\\Leftrightarrow &-14x & = &6\\\Leftrightarrow & \color{red}{-14}x & = &6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)