Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-9}& = &8 \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9} & = &8\color{blue}{+9} \\\Leftrightarrow &-11x & = &17\\\Leftrightarrow & \color{red}{-11}x & = &17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-11}& = &13 \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11} & = &13\color{blue}{+11} \\\Leftrightarrow &-4x & = &24\\\Leftrightarrow & \color{red}{-4}x & = &24\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{24}{-4} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-14}& = &-12 \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14} & = &-12\color{blue}{+14} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+3}& = &7 \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3} & = &7\color{blue}{-3} \\\Leftrightarrow &14x & = &4\\\Leftrightarrow & \color{red}{14}x & = &4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-5}& = &-7 \\\Leftrightarrow & x \color{red}{-5}\color{blue}{+5} & = &-7\color{blue}{+5} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-4}& = &4 \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4} & = &4\color{blue}{+4} \\\Leftrightarrow &-x & = &8\\\Leftrightarrow & \color{red}{-}x & = &8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{8}{-1} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+5}& = &-12 \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5} & = &-12\color{blue}{-5} \\\Leftrightarrow &x & = &-17\\\Leftrightarrow & \color{red}{}x & = &-17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -17 \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-5}& = &-6 \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5} & = &-6\color{blue}{+5} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+4}& = &5 \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4} & = &5\color{blue}{-4} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+8}& = &-7 \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8} & = &-7\color{blue}{-8} \\\Leftrightarrow &3x & = &-15\\\Leftrightarrow & \color{red}{3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-15}{3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+11}& = &-2 \\\Leftrightarrow & x \color{red}{+11}\color{blue}{-11} & = &-2\color{blue}{-11} \\\Leftrightarrow &x & = &-13\\\Leftrightarrow & \color{red}{}x & = &-13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -13 \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{-14}& = &13 \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14} & = &13\color{blue}{+14} \\\Leftrightarrow &14x & = &27\\\Leftrightarrow & \color{red}{14}x & = &27\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{27}{14} \\\Leftrightarrow & \color{green}{ x = \frac{27}{14} } & & \\ & V = \left\{ \frac{27}{14} \right\} & \\\end{align}\)