Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-10}& = &-5 \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10} & = &-5\color{blue}{+10} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+8}& = &-6 \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8} & = &-6\color{blue}{-8} \\\Leftrightarrow &6x & = &-14\\\Leftrightarrow & \color{red}{6}x & = &-14\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-14}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-4}& = &-8 \\\Leftrightarrow & -14x \color{red}{-4}\color{blue}{+4} & = &-8\color{blue}{+4} \\\Leftrightarrow &-14x & = &-4\\\Leftrightarrow & \color{red}{-14}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-3}& = &-9 \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3} & = &-9\color{blue}{+3} \\\Leftrightarrow &13x & = &-6\\\Leftrightarrow & \color{red}{13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-2}& = &-2 \\\Leftrightarrow & -12x \color{red}{-2}\color{blue}{+2} & = &-2\color{blue}{+2} \\\Leftrightarrow &-12x & = &0\\\Leftrightarrow & \color{red}{-12}x & = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+1}& = &-9 \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1} & = &-9\color{blue}{-1} \\\Leftrightarrow &15x & = &-10\\\Leftrightarrow & \color{red}{15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-10}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+13}& = &-12 \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13} & = &-12\color{blue}{-13} \\\Leftrightarrow &-5x & = &-25\\\Leftrightarrow & \color{red}{-5}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-25}{-5} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-7}& = &-7 \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7} & = &-7\color{blue}{+7} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-14}& = &-2 \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14} & = &-2\color{blue}{+14} \\\Leftrightarrow &-6x & = &12\\\Leftrightarrow & \color{red}{-6}x & = &12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{12}{-6} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+12}& = &-15 \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12} & = &-15\color{blue}{-12} \\\Leftrightarrow &-14x & = &-27\\\Leftrightarrow & \color{red}{-14}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-27}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{27}{14} } & & \\ & V = \left\{ \frac{27}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+6}& = &7 \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6} & = &7\color{blue}{-6} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+2}& = &-9 \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2} & = &-9\color{blue}{-2} \\\Leftrightarrow &10x & = &-11\\\Leftrightarrow & \color{red}{10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)