Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+14}& = &-8 \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14} & = &-8\color{blue}{-14} \\\Leftrightarrow &13x & = &-22\\\Leftrightarrow & \color{red}{13}x & = &-22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{13} } & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-6}& = &-1 \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6} & = &-1\color{blue}{+6} \\\Leftrightarrow &-4x & = &5\\\Leftrightarrow & \color{red}{-4}x & = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+3}& = &12 \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3} & = &12\color{blue}{-3} \\\Leftrightarrow &6x & = &9\\\Leftrightarrow & \color{red}{6}x & = &9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-3}& = &-1 \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3} & = &-1\color{blue}{+3} \\\Leftrightarrow &10x & = &2\\\Leftrightarrow & \color{red}{10}x & = &2\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{2}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+11}& = &2 \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11} & = &2\color{blue}{-11} \\\Leftrightarrow &10x & = &-9\\\Leftrightarrow & \color{red}{10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-9}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+14}& = &-13 \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14} & = &-13\color{blue}{-14} \\\Leftrightarrow &8x & = &-27\\\Leftrightarrow & \color{red}{8}x & = &-27\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-27}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{8} } & & \\ & V = \left\{ \frac{-27}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+6}& = &-1 \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6} & = &-1\color{blue}{-6} \\\Leftrightarrow &-2x & = &-7\\\Leftrightarrow & \color{red}{-2}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-7}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-1}& = &-6 \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1} & = &-6\color{blue}{+1} \\\Leftrightarrow &-13x & = &-5\\\Leftrightarrow & \color{red}{-13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-10}& = &11 \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10} & = &11\color{blue}{+10} \\\Leftrightarrow &6x & = &21\\\Leftrightarrow & \color{red}{6}x & = &21\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{21}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+13}& = &-2 \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13} & = &-2\color{blue}{-13} \\\Leftrightarrow &4x & = &-15\\\Leftrightarrow & \color{red}{4}x & = &-15\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-15}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{4} } & & \\ & V = \left\{ \frac{-15}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+11}& = &14 \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11} & = &14\color{blue}{-11} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-5}& = &-4 \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5} & = &-4\color{blue}{+5} \\\Leftrightarrow &6x & = &1\\\Leftrightarrow & \color{red}{6}x & = &1\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{1}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)