Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-11}& = &2 \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11} & = &2\color{blue}{+11} \\\Leftrightarrow &-11x & = &13\\\Leftrightarrow & \color{red}{-11}x & = &13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+1}& = &13 \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1} & = &13\color{blue}{-1} \\\Leftrightarrow &-12x & = &12\\\Leftrightarrow & \color{red}{-12}x & = &12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{12}{-12} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-3}& = &7 \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3} & = &7\color{blue}{+3} \\\Leftrightarrow &-4x & = &10\\\Leftrightarrow & \color{red}{-4}x & = &10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+14}& = &6 \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14} & = &6\color{blue}{-14} \\\Leftrightarrow &-10x & = &-8\\\Leftrightarrow & \color{red}{-10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-5}& = &7 \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5} & = &7\color{blue}{+5} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+1}& = &2 \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1} & = &2\color{blue}{-1} \\\Leftrightarrow &-9x & = &1\\\Leftrightarrow & \color{red}{-9}x & = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+13}& = &5 \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13} & = &5\color{blue}{-13} \\\Leftrightarrow &12x & = &-8\\\Leftrightarrow & \color{red}{12}x & = &-8\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-8}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-15}& = &-3 \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15} & = &-3\color{blue}{+15} \\\Leftrightarrow &10x & = &12\\\Leftrightarrow & \color{red}{10}x & = &12\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{12}{10} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+14}& = &-15 \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14} & = &-15\color{blue}{-14} \\\Leftrightarrow &11x & = &-29\\\Leftrightarrow & \color{red}{11}x & = &-29\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-29}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{11} } & & \\ & V = \left\{ \frac{-29}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-15}& = &-5 \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15} & = &-5\color{blue}{+15} \\\Leftrightarrow &13x & = &10\\\Leftrightarrow & \color{red}{13}x & = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{+5}& = &6 \\\Leftrightarrow & 2x \color{red}{+5}\color{blue}{-5} & = &6\color{blue}{-5} \\\Leftrightarrow &2x & = &1\\\Leftrightarrow & \color{red}{2}x & = &1\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{1}{2} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+10}& = &9 \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10} & = &9\color{blue}{-10} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)