Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+14}& = &-6 \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14} & = &-6\color{blue}{-14} \\\Leftrightarrow &-6x & = &-20\\\Leftrightarrow & \color{red}{-6}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-20}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-11}& = &3 \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11} & = &3\color{blue}{+11} \\\Leftrightarrow &10x & = &14\\\Leftrightarrow & \color{red}{10}x & = &14\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{14}{10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-7}& = &-14 \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7} & = &-14\color{blue}{+7} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+15}& = &9 \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15} & = &9\color{blue}{-15} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+15}& = &-12 \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15} & = &-12\color{blue}{-15} \\\Leftrightarrow &9x & = &-27\\\Leftrightarrow & \color{red}{9}x & = &-27\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-27}{9} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-13}& = &-3 \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13} & = &-3\color{blue}{+13} \\\Leftrightarrow &2x & = &10\\\Leftrightarrow & \color{red}{2}x & = &10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{10}{2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-4}& = &6 \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4} & = &6\color{blue}{+4} \\\Leftrightarrow &-15x & = &10\\\Leftrightarrow & \color{red}{-15}x & = &10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+5}& = &-8 \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5} & = &-8\color{blue}{-5} \\\Leftrightarrow &-14x & = &-13\\\Leftrightarrow & \color{red}{-14}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-13}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-13}& = &-15 \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13} & = &-15\color{blue}{+13} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-7}& = &5 \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7} & = &5\color{blue}{+7} \\\Leftrightarrow &6x & = &12\\\Leftrightarrow & \color{red}{6}x & = &12\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{12}{6} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+7}& = &1 \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7} & = &1\color{blue}{-7} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+10}& = &-4 \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10} & = &-4\color{blue}{-10} \\\Leftrightarrow &-2x & = &-14\\\Leftrightarrow & \color{red}{-2}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-14}{-2} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)