Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-14}& = &6 \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14} & = &6\color{blue}{+14} \\\Leftrightarrow &6x & = &20\\\Leftrightarrow & \color{red}{6}x & = &20\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{20}{6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+3}& = &3 \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3} & = &3\color{blue}{-3} \\\Leftrightarrow &2x & = &0\\\Leftrightarrow & \color{red}{2}x & = &0\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{0}{2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-13}& = &-3 \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13} & = &-3\color{blue}{+13} \\\Leftrightarrow &11x & = &10\\\Leftrightarrow & \color{red}{11}x & = &10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-4}& = &15 \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4} & = &15\color{blue}{+4} \\\Leftrightarrow &-11x & = &19\\\Leftrightarrow & \color{red}{-11}x & = &19\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{19}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{11} } & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+14}& = &-4 \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14} & = &-4\color{blue}{-14} \\\Leftrightarrow &8x & = &-18\\\Leftrightarrow & \color{red}{8}x & = &-18\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-18}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+13}& = &13 \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13} & = &13\color{blue}{-13} \\\Leftrightarrow &4x & = &0\\\Leftrightarrow & \color{red}{4}x & = &0\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{0}{4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-4}& = &-1 \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4} & = &-1\color{blue}{+4} \\\Leftrightarrow &9x & = &3\\\Leftrightarrow & \color{red}{9}x & = &3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-14}& = &8 \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14} & = &8\color{blue}{+14} \\\Leftrightarrow &9x & = &22\\\Leftrightarrow & \color{red}{9}x & = &22\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{22}{9} \\\Leftrightarrow & \color{green}{ x = \frac{22}{9} } & & \\ & V = \left\{ \frac{22}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+13}& = &13 \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13} & = &13\color{blue}{-13} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-10}& = &10 \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10} & = &10\color{blue}{+10} \\\Leftrightarrow &5x & = &20\\\Leftrightarrow & \color{red}{5}x & = &20\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{20}{5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+9}& = &10 \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9} & = &10\color{blue}{-9} \\\Leftrightarrow &9x & = &1\\\Leftrightarrow & \color{red}{9}x & = &1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-7}& = &-2 \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7} & = &-2\color{blue}{+7} \\\Leftrightarrow &8x & = &5\\\Leftrightarrow & \color{red}{8}x & = &5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)