Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-13}& = &6 \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13} & = &6\color{blue}{+13} \\\Leftrightarrow &13x & = &19\\\Leftrightarrow & \color{red}{13}x & = &19\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{19}{13} \\\Leftrightarrow & \color{green}{ x = \frac{19}{13} } & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-14}& = &10 \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14} & = &10\color{blue}{+14} \\\Leftrightarrow &-15x & = &24\\\Leftrightarrow & \color{red}{-15}x & = &24\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{24}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+9}& = &11 \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9} & = &11\color{blue}{-9} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-12}& = &-8 \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12} & = &-8\color{blue}{+12} \\\Leftrightarrow &5x & = &4\\\Leftrightarrow & \color{red}{5}x & = &4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+9}& = &12 \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9} & = &12\color{blue}{-9} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-7}& = &-14 \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7} & = &-14\color{blue}{+7} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+4}& = &-7 \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4} & = &-7\color{blue}{-4} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+6}& = &-11 \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6} & = &-11\color{blue}{-6} \\\Leftrightarrow &-4x & = &-17\\\Leftrightarrow & \color{red}{-4}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-17}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{17}{4} } & & \\ & V = \left\{ \frac{17}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-7}& = &12 \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7} & = &12\color{blue}{+7} \\\Leftrightarrow &2x & = &19\\\Leftrightarrow & \color{red}{2}x & = &19\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{19}{2} \\\Leftrightarrow & \color{green}{ x = \frac{19}{2} } & & \\ & V = \left\{ \frac{19}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+10}& = &-1 \\\Leftrightarrow & -13x \color{red}{+10}\color{blue}{-10} & = &-1\color{blue}{-10} \\\Leftrightarrow &-13x & = &-11\\\Leftrightarrow & \color{red}{-13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+7}& = &-7 \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7} & = &-7\color{blue}{-7} \\\Leftrightarrow &14x & = &-14\\\Leftrightarrow & \color{red}{14}x & = &-14\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-14}{14} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-6}& = &-10 \\\Leftrightarrow & 6x \color{red}{-6}\color{blue}{+6} & = &-10\color{blue}{+6} \\\Leftrightarrow &6x & = &-4\\\Leftrightarrow & \color{red}{6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-4}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)