Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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