Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+4}& = &6 \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4} & = &6\color{blue}{-4} \\\Leftrightarrow &2x & = &2\\\Leftrightarrow & \color{red}{2}x & = &2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{2}{2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+12}& = &8 \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12} & = &8\color{blue}{-12} \\\Leftrightarrow &-8x & = &-4\\\Leftrightarrow & \color{red}{-8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+6}& = &-10 \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6} & = &-10\color{blue}{-6} \\\Leftrightarrow &13x & = &-16\\\Leftrightarrow & \color{red}{13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+9}& = &-13 \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9} & = &-13\color{blue}{-9} \\\Leftrightarrow &11x & = &-22\\\Leftrightarrow & \color{red}{11}x & = &-22\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-22}{11} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-12}& = &15 \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12} & = &15\color{blue}{+12} \\\Leftrightarrow &13x & = &27\\\Leftrightarrow & \color{red}{13}x & = &27\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{27}{13} \\\Leftrightarrow & \color{green}{ x = \frac{27}{13} } & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+5}& = &2 \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5} & = &2\color{blue}{-5} \\\Leftrightarrow &-13x & = &-3\\\Leftrightarrow & \color{red}{-13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+9}& = &12 \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9} & = &12\color{blue}{-9} \\\Leftrightarrow &6x & = &3\\\Leftrightarrow & \color{red}{6}x & = &3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+1}& = &-1 \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1} & = &-1\color{blue}{-1} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+13}& = &9 \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13} & = &9\color{blue}{-13} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-12}& = &10 \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12} & = &10\color{blue}{+12} \\\Leftrightarrow &5x & = &22\\\Leftrightarrow & \color{red}{5}x & = &22\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{22}{5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+4}& = &7 \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4} & = &7\color{blue}{-4} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+10}& = &-5 \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10} & = &-5\color{blue}{-10} \\\Leftrightarrow &11x & = &-15\\\Leftrightarrow & \color{red}{11}x & = &-15\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-15}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)