Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+9}& = &10 \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9} & = &10\color{blue}{-9} \\\Leftrightarrow &-9x & = &1\\\Leftrightarrow & \color{red}{-9}x & = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+14}& = &-9 \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14} & = &-9\color{blue}{-14} \\\Leftrightarrow &14x & = &-23\\\Leftrightarrow & \color{red}{14}x & = &-23\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-23}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{14} } & & \\ & V = \left\{ \frac{-23}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-14}& = &-5 \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14} & = &-5\color{blue}{+14} \\\Leftrightarrow &-2x & = &9\\\Leftrightarrow & \color{red}{-2}x & = &9\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{9}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-15}& = &15 \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15} & = &15\color{blue}{+15} \\\Leftrightarrow &-3x & = &30\\\Leftrightarrow & \color{red}{-3}x & = &30\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{30}{-3} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-11}& = &-15 \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11} & = &-15\color{blue}{+11} \\\Leftrightarrow &13x & = &-4\\\Leftrightarrow & \color{red}{13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+1}& = &8 \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1} & = &8\color{blue}{-1} \\\Leftrightarrow &9x & = &7\\\Leftrightarrow & \color{red}{9}x & = &7\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{7}{9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-8}& = &4 \\\Leftrightarrow & -6x \color{red}{-8}\color{blue}{+8} & = &4\color{blue}{+8} \\\Leftrightarrow &-6x & = &12\\\Leftrightarrow & \color{red}{-6}x & = &12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{12}{-6} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+6}& = &-2 \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6} & = &-2\color{blue}{-6} \\\Leftrightarrow &8x & = &-8\\\Leftrightarrow & \color{red}{8}x & = &-8\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-8}{8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-13}& = &1 \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13} & = &1\color{blue}{+13} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-7}& = &15 \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7} & = &15\color{blue}{+7} \\\Leftrightarrow &10x & = &22\\\Leftrightarrow & \color{red}{10}x & = &22\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{22}{10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-14}& = &15 \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14} & = &15\color{blue}{+14} \\\Leftrightarrow &14x & = &29\\\Leftrightarrow & \color{red}{14}x & = &29\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{29}{14} \\\Leftrightarrow & \color{green}{ x = \frac{29}{14} } & & \\ & V = \left\{ \frac{29}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{+10}& = &-1 \\\Leftrightarrow & 8x \color{red}{+10}\color{blue}{-10} & = &-1\color{blue}{-10} \\\Leftrightarrow &8x & = &-11\\\Leftrightarrow & \color{red}{8}x & = &-11\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-11}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)