Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-12}& = &9 \\\Leftrightarrow & 10x \color{red}{-12}\color{blue}{+12} & = &9\color{blue}{+12} \\\Leftrightarrow &10x & = &21\\\Leftrightarrow & \color{red}{10}x & = &21\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{21}{10} \\\Leftrightarrow & \color{green}{ x = \frac{21}{10} } & & \\ & V = \left\{ \frac{21}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+2}& = &-15 \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2} & = &-15\color{blue}{-2} \\\Leftrightarrow &6x & = &-17\\\Leftrightarrow & \color{red}{6}x & = &-17\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-17}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{6} } & & \\ & V = \left\{ \frac{-17}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-11}& = &3 \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11} & = &3\color{blue}{+11} \\\Leftrightarrow &2x & = &14\\\Leftrightarrow & \color{red}{2}x & = &14\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{14}{2} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{+4}& = &6 \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4} & = &6\color{blue}{-4} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-6}& = &-14 \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6} & = &-14\color{blue}{+6} \\\Leftrightarrow &-7x & = &-8\\\Leftrightarrow & \color{red}{-7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-5}& = &-12 \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5} & = &-12\color{blue}{+5} \\\Leftrightarrow &2x & = &-7\\\Leftrightarrow & \color{red}{2}x & = &-7\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-7}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+4}& = &12 \\\Leftrightarrow & -11x \color{red}{+4}\color{blue}{-4} & = &12\color{blue}{-4} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-10}& = &-15 \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10} & = &-15\color{blue}{+10} \\\Leftrightarrow &9x & = &-5\\\Leftrightarrow & \color{red}{9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-10}& = &12 \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10} & = &12\color{blue}{+10} \\\Leftrightarrow &-x & = &22\\\Leftrightarrow & \color{red}{-}x & = &22\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{22}{-1} \\\Leftrightarrow & \color{green}{ x = -22 } & & \\ & V = \left\{ -22 \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-10}& = &14 \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10} & = &14\color{blue}{+10} \\\Leftrightarrow &5x & = &24\\\Leftrightarrow & \color{red}{5}x & = &24\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{24}{5} \\\Leftrightarrow & \color{green}{ x = \frac{24}{5} } & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-9}& = &-2 \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9} & = &-2\color{blue}{+9} \\\Leftrightarrow &9x & = &7\\\Leftrightarrow & \color{red}{9}x & = &7\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{7}{9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-13}& = &-14 \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13} & = &-14\color{blue}{+13} \\\Leftrightarrow &6x & = &-1\\\Leftrightarrow & \color{red}{6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-1}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)