Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+14}& = &14 \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14} & = &14\color{blue}{-14} \\\Leftrightarrow &9x & = &0\\\Leftrightarrow & \color{red}{9}x & = &0\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{0}{9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{+13}& = &13 \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13} & = &13\color{blue}{-13} \\\Leftrightarrow &13x & = &0\\\Leftrightarrow & \color{red}{13}x & = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-14}& = &-8 \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14} & = &-8\color{blue}{+14} \\\Leftrightarrow &-4x & = &6\\\Leftrightarrow & \color{red}{-4}x & = &6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-7}& = &1 \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7} & = &1\color{blue}{+7} \\\Leftrightarrow &-6x & = &8\\\Leftrightarrow & \color{red}{-6}x & = &8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-12}& = &-15 \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12} & = &-15\color{blue}{+12} \\\Leftrightarrow &8x & = &-3\\\Leftrightarrow & \color{red}{8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+13}& = &7 \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13} & = &7\color{blue}{-13} \\\Leftrightarrow &9x & = &-6\\\Leftrightarrow & \color{red}{9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+14}& = &-1 \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14} & = &-1\color{blue}{-14} \\\Leftrightarrow &7x & = &-15\\\Leftrightarrow & \color{red}{7}x & = &-15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+10}& = &5 \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10} & = &5\color{blue}{-10} \\\Leftrightarrow &14x & = &-5\\\Leftrightarrow & \color{red}{14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-5}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+3}& = &14 \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3} & = &14\color{blue}{-3} \\\Leftrightarrow &5x & = &11\\\Leftrightarrow & \color{red}{5}x & = &11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-13}& = &10 \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13} & = &10\color{blue}{+13} \\\Leftrightarrow &-12x & = &23\\\Leftrightarrow & \color{red}{-12}x & = &23\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{23}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{12} } & & \\ & V = \left\{ \frac{-23}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-8}& = &6 \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8} & = &6\color{blue}{+8} \\\Leftrightarrow &-13x & = &14\\\Leftrightarrow & \color{red}{-13}x & = &14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+3}& = &-9 \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3} & = &-9\color{blue}{-3} \\\Leftrightarrow &4x & = &-12\\\Leftrightarrow & \color{red}{4}x & = &-12\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-12}{4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)