Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-14}& = &15 \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14} & = &15\color{blue}{+14} \\\Leftrightarrow &-13x & = &29\\\Leftrightarrow & \color{red}{-13}x & = &29\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{29}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{13} } & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+6}& = &-2 \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6} & = &-2\color{blue}{-6} \\\Leftrightarrow &9x & = &-8\\\Leftrightarrow & \color{red}{9}x & = &-8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+3}& = &1 \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3} & = &1\color{blue}{-3} \\\Leftrightarrow &-5x & = &-2\\\Leftrightarrow & \color{red}{-5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+15}& = &-1 \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15} & = &-1\color{blue}{-15} \\\Leftrightarrow &-13x & = &-16\\\Leftrightarrow & \color{red}{-13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+3}& = &-8 \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3} & = &-8\color{blue}{-3} \\\Leftrightarrow &10x & = &-11\\\Leftrightarrow & \color{red}{10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-13}& = &-4 \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13} & = &-4\color{blue}{+13} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+2}& = &-7 \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2} & = &-7\color{blue}{-2} \\\Leftrightarrow &6x & = &-9\\\Leftrightarrow & \color{red}{6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-2}& = &-11 \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2} & = &-11\color{blue}{+2} \\\Leftrightarrow &7x & = &-9\\\Leftrightarrow & \color{red}{7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+9}& = &3 \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9} & = &3\color{blue}{-9} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-4}& = &4 \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4} & = &4\color{blue}{+4} \\\Leftrightarrow &-x & = &8\\\Leftrightarrow & \color{red}{-}x & = &8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{8}{-1} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+9}& = &-11 \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9} & = &-11\color{blue}{-9} \\\Leftrightarrow &-13x & = &-20\\\Leftrightarrow & \color{red}{-13}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-14}& = &11 \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14} & = &11\color{blue}{+14} \\\Leftrightarrow &x & = &25\\\Leftrightarrow & \color{red}{}x & = &25\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 25 \\\Leftrightarrow & \color{green}{ x = 25 } & & \\ & V = \left\{ 25 \right\} & \\\end{align}\)