Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & x \color{red}{+1}& = &-15 \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1} & = &-15\color{blue}{-1} \\\Leftrightarrow &x & = &-16\\\Leftrightarrow & \color{red}{}x & = &-16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -16 \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-8}& = &-13 \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8} & = &-13\color{blue}{+8} \\\Leftrightarrow &10x & = &-5\\\Leftrightarrow & \color{red}{10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-5}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+3}& = &10 \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3} & = &10\color{blue}{-3} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-6}& = &-8 \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6} & = &-8\color{blue}{+6} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-14}& = &12 \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14} & = &12\color{blue}{+14} \\\Leftrightarrow &8x & = &26\\\Leftrightarrow & \color{red}{8}x & = &26\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{26}{8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+13}& = &10 \\\Leftrightarrow & 7x \color{red}{+13}\color{blue}{-13} & = &10\color{blue}{-13} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-6}& = &-14 \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6} & = &-14\color{blue}{+6} \\\Leftrightarrow &-8x & = &-8\\\Leftrightarrow & \color{red}{-8}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-8}{-8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-15}& = &10 \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15} & = &10\color{blue}{+15} \\\Leftrightarrow &-4x & = &25\\\Leftrightarrow & \color{red}{-4}x & = &25\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{25}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{4} } & & \\ & V = \left\{ \frac{-25}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+6}& = &8 \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6} & = &8\color{blue}{-6} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-4}& = &-2 \\\Leftrightarrow & -14x \color{red}{-4}\color{blue}{+4} & = &-2\color{blue}{+4} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-14}& = &9 \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14} & = &9\color{blue}{+14} \\\Leftrightarrow &-3x & = &23\\\Leftrightarrow & \color{red}{-3}x & = &23\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{23}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{3} } & & \\ & V = \left\{ \frac{-23}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+3}& = &9 \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3} & = &9\color{blue}{-3} \\\Leftrightarrow &-14x & = &6\\\Leftrightarrow & \color{red}{-14}x & = &6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)