Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+1}& = &1 \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1} & = &1\color{blue}{-1} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-12}& = &-11 \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12} & = &-11\color{blue}{+12} \\\Leftrightarrow &9x & = &1\\\Leftrightarrow & \color{red}{9}x & = &1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+10}& = &-6 \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10} & = &-6\color{blue}{-10} \\\Leftrightarrow &11x & = &-16\\\Leftrightarrow & \color{red}{11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-1}& = &-4 \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1} & = &-4\color{blue}{+1} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-14}& = &-8 \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14} & = &-8\color{blue}{+14} \\\Leftrightarrow &9x & = &6\\\Leftrightarrow & \color{red}{9}x & = &6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-13}& = &11 \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13} & = &11\color{blue}{+13} \\\Leftrightarrow &-2x & = &24\\\Leftrightarrow & \color{red}{-2}x & = &24\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{24}{-2} \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+4}& = &1 \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4} & = &1\color{blue}{-4} \\\Leftrightarrow &-5x & = &-3\\\Leftrightarrow & \color{red}{-5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-9}& = &15 \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9} & = &15\color{blue}{+9} \\\Leftrightarrow &-8x & = &24\\\Leftrightarrow & \color{red}{-8}x & = &24\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{24}{-8} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-11}& = &-5 \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11} & = &-5\color{blue}{+11} \\\Leftrightarrow &3x & = &6\\\Leftrightarrow & \color{red}{3}x & = &6\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{6}{3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-10}& = &7 \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10} & = &7\color{blue}{+10} \\\Leftrightarrow &-6x & = &17\\\Leftrightarrow & \color{red}{-6}x & = &17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{6} } & & \\ & V = \left\{ \frac{-17}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-5}& = &-1 \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5} & = &-1\color{blue}{+5} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-15}& = &2 \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15} & = &2\color{blue}{+15} \\\Leftrightarrow &13x & = &17\\\Leftrightarrow & \color{red}{13}x & = &17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)