Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-12}& = &-6 \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12} & = &-6\color{blue}{+12} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-14}& = &-2 \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14} & = &-2\color{blue}{+14} \\\Leftrightarrow &14x & = &12\\\Leftrightarrow & \color{red}{14}x & = &12\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{12}{14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+15}& = &-11 \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15} & = &-11\color{blue}{-15} \\\Leftrightarrow &9x & = &-26\\\Leftrightarrow & \color{red}{9}x & = &-26\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-26}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{9} } & & \\ & V = \left\{ \frac{-26}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-2}& = &-2 \\\Leftrightarrow & -9x \color{red}{-2}\color{blue}{+2} & = &-2\color{blue}{+2} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+13}& = &-14 \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13} & = &-14\color{blue}{-13} \\\Leftrightarrow &5x & = &-27\\\Leftrightarrow & \color{red}{5}x & = &-27\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-27}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{5} } & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+1}& = &7 \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1} & = &7\color{blue}{-1} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+1}& = &4 \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1} & = &4\color{blue}{-1} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-9}& = &7 \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9} & = &7\color{blue}{+9} \\\Leftrightarrow &7x & = &16\\\Leftrightarrow & \color{red}{7}x & = &16\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{16}{7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{+3}& = &-1 \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3} & = &-1\color{blue}{-3} \\\Leftrightarrow &-14x & = &-4\\\Leftrightarrow & \color{red}{-14}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-4}& = &7 \\\Leftrightarrow & -14x \color{red}{-4}\color{blue}{+4} & = &7\color{blue}{+4} \\\Leftrightarrow &-14x & = &11\\\Leftrightarrow & \color{red}{-14}x & = &11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-9}& = &15 \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9} & = &15\color{blue}{+9} \\\Leftrightarrow &-5x & = &24\\\Leftrightarrow & \color{red}{-5}x & = &24\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{24}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{5} } & & \\ & V = \left\{ \frac{-24}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-5}& = &-3 \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5} & = &-3\color{blue}{+5} \\\Leftrightarrow &13x & = &2\\\Leftrightarrow & \color{red}{13}x & = &2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)