Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+11}& = &1 \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11} & = &1\color{blue}{-11} \\\Leftrightarrow &12x & = &-10\\\Leftrightarrow & \color{red}{12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-10}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-10}& = &-6 \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10} & = &-6\color{blue}{+10} \\\Leftrightarrow &6x & = &4\\\Leftrightarrow & \color{red}{6}x & = &4\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{4}{6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+5}& = &-1 \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5} & = &-1\color{blue}{-5} \\\Leftrightarrow &9x & = &-6\\\Leftrightarrow & \color{red}{9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{+6}& = &-3 \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6} & = &-3\color{blue}{-6} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-2}& = &14 \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2} & = &14\color{blue}{+2} \\\Leftrightarrow &13x & = &16\\\Leftrightarrow & \color{red}{13}x & = &16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+12}& = &7 \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12} & = &7\color{blue}{-12} \\\Leftrightarrow &3x & = &-5\\\Leftrightarrow & \color{red}{3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+13}& = &10 \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13} & = &10\color{blue}{-13} \\\Leftrightarrow &8x & = &-3\\\Leftrightarrow & \color{red}{8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+8}& = &-13 \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8} & = &-13\color{blue}{-8} \\\Leftrightarrow &3x & = &-21\\\Leftrightarrow & \color{red}{3}x & = &-21\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-21}{3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+10}& = &-7 \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10} & = &-7\color{blue}{-10} \\\Leftrightarrow &-10x & = &-17\\\Leftrightarrow & \color{red}{-10}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{17}{10} } & & \\ & V = \left\{ \frac{17}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-12}& = &-4 \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12} & = &-4\color{blue}{+12} \\\Leftrightarrow &3x & = &8\\\Leftrightarrow & \color{red}{3}x & = &8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-4}& = &13 \\\Leftrightarrow & 11x \color{red}{-4}\color{blue}{+4} & = &13\color{blue}{+4} \\\Leftrightarrow &11x & = &17\\\Leftrightarrow & \color{red}{11}x & = &17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+14}& = &8 \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14} & = &8\color{blue}{-14} \\\Leftrightarrow &6x & = &-6\\\Leftrightarrow & \color{red}{6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-6}{6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)