Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+11}& = &7 \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11} & = &7\color{blue}{-11} \\\Leftrightarrow &-4x & = &-4\\\Leftrightarrow & \color{red}{-4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-14}& = &-15 \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14} & = &-15\color{blue}{+14} \\\Leftrightarrow &15x & = &-1\\\Leftrightarrow & \color{red}{15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+8}& = &-10 \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8} & = &-10\color{blue}{-8} \\\Leftrightarrow &-11x & = &-18\\\Leftrightarrow & \color{red}{-11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-3}& = &14 \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3} & = &14\color{blue}{+3} \\\Leftrightarrow &11x & = &17\\\Leftrightarrow & \color{red}{11}x & = &17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+15}& = &-5 \\\Leftrightarrow & x \color{red}{+15}\color{blue}{-15} & = &-5\color{blue}{-15} \\\Leftrightarrow &x & = &-20\\\Leftrightarrow & \color{red}{}x & = &-20\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -20 \\\Leftrightarrow & \color{green}{ x = -20 } & & \\ & V = \left\{ -20 \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-8}& = &6 \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8} & = &6\color{blue}{+8} \\\Leftrightarrow &-5x & = &14\\\Leftrightarrow & \color{red}{-5}x & = &14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{5} } & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+3}& = &5 \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3} & = &5\color{blue}{-3} \\\Leftrightarrow &-12x & = &2\\\Leftrightarrow & \color{red}{-12}x & = &2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-6}& = &-3 \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6} & = &-3\color{blue}{+6} \\\Leftrightarrow &-8x & = &3\\\Leftrightarrow & \color{red}{-8}x & = &3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+8}& = &11 \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8} & = &11\color{blue}{-8} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+2}& = &-14 \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2} & = &-14\color{blue}{-2} \\\Leftrightarrow &10x & = &-16\\\Leftrightarrow & \color{red}{10}x & = &-16\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-16}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-7}& = &-6 \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7} & = &-6\color{blue}{+7} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+13}& = &-12 \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13} & = &-12\color{blue}{-13} \\\Leftrightarrow &-13x & = &-25\\\Leftrightarrow & \color{red}{-13}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-25}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{25}{13} } & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)