Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+12}& = &7 \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12} & = &7\color{blue}{-12} \\\Leftrightarrow &13x & = &-5\\\Leftrightarrow & \color{red}{13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{-4}& = &-15 \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4} & = &-15\color{blue}{+4} \\\Leftrightarrow &13x & = &-11\\\Leftrightarrow & \color{red}{13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-1}& = &9 \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1} & = &9\color{blue}{+1} \\\Leftrightarrow &9x & = &10\\\Leftrightarrow & \color{red}{9}x & = &10\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{10}{9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-13}& = &6 \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13} & = &6\color{blue}{+13} \\\Leftrightarrow &10x & = &19\\\Leftrightarrow & \color{red}{10}x & = &19\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{19}{10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-11}& = &6 \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11} & = &6\color{blue}{+11} \\\Leftrightarrow &-8x & = &17\\\Leftrightarrow & \color{red}{-8}x & = &17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{8} } & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+13}& = &-9 \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13} & = &-9\color{blue}{-13} \\\Leftrightarrow &-10x & = &-22\\\Leftrightarrow & \color{red}{-10}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-22}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-11}& = &15 \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11} & = &15\color{blue}{+11} \\\Leftrightarrow &-6x & = &26\\\Leftrightarrow & \color{red}{-6}x & = &26\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{26}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-6}& = &14 \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6} & = &14\color{blue}{+6} \\\Leftrightarrow &14x & = &20\\\Leftrightarrow & \color{red}{14}x & = &20\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{20}{14} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+9}& = &-4 \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9} & = &-4\color{blue}{-9} \\\Leftrightarrow &-13x & = &-13\\\Leftrightarrow & \color{red}{-13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+11}& = &-14 \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11} & = &-14\color{blue}{-11} \\\Leftrightarrow &5x & = &-25\\\Leftrightarrow & \color{red}{5}x & = &-25\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-25}{5} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+8}& = &-6 \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8} & = &-6\color{blue}{-8} \\\Leftrightarrow &14x & = &-14\\\Leftrightarrow & \color{red}{14}x & = &-14\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-14}{14} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+10}& = &4 \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10} & = &4\color{blue}{-10} \\\Leftrightarrow &-12x & = &-6\\\Leftrightarrow & \color{red}{-12}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)