Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-9}& = &7 \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9} & = &7\color{blue}{+9} \\\Leftrightarrow &-x & = &16\\\Leftrightarrow & \color{red}{-}x & = &16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{16}{-1} \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+7}& = &1 \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7} & = &1\color{blue}{-7} \\\Leftrightarrow &12x & = &-6\\\Leftrightarrow & \color{red}{12}x & = &-6\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-6}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+8}& = &9 \\\Leftrightarrow & -5x \color{red}{+8}\color{blue}{-8} & = &9\color{blue}{-8} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+5}& = &-13 \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5} & = &-13\color{blue}{-5} \\\Leftrightarrow &-14x & = &-18\\\Leftrightarrow & \color{red}{-14}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-9}& = &13 \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9} & = &13\color{blue}{+9} \\\Leftrightarrow &-9x & = &22\\\Leftrightarrow & \color{red}{-9}x & = &22\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{22}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{9} } & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+15}& = &-10 \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15} & = &-10\color{blue}{-15} \\\Leftrightarrow &10x & = &-25\\\Leftrightarrow & \color{red}{10}x & = &-25\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-25}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-1}& = &1 \\\Leftrightarrow & -2x \color{red}{-1}\color{blue}{+1} & = &1\color{blue}{+1} \\\Leftrightarrow &-2x & = &2\\\Leftrightarrow & \color{red}{-2}x & = &2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{2}{-2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-4}& = &-5 \\\Leftrightarrow & 11x \color{red}{-4}\color{blue}{+4} & = &-5\color{blue}{+4} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+7}& = &-15 \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7} & = &-15\color{blue}{-7} \\\Leftrightarrow &10x & = &-22\\\Leftrightarrow & \color{red}{10}x & = &-22\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-22}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-4}& = &10 \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4} & = &10\color{blue}{+4} \\\Leftrightarrow &-12x & = &14\\\Leftrightarrow & \color{red}{-12}x & = &14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+5}& = &9 \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5} & = &9\color{blue}{-5} \\\Leftrightarrow &3x & = &4\\\Leftrightarrow & \color{red}{3}x & = &4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-11}& = &15 \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11} & = &15\color{blue}{+11} \\\Leftrightarrow &12x & = &26\\\Leftrightarrow & \color{red}{12}x & = &26\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{26}{12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)