Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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