Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+6}& = &9 \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6} & = &9\color{blue}{-6} \\\Leftrightarrow &-8x & = &3\\\Leftrightarrow & \color{red}{-8}x & = &3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-6}& = &-8 \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6} & = &-8\color{blue}{+6} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+11}& = &-9 \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11} & = &-9\color{blue}{-11} \\\Leftrightarrow &2x & = &-20\\\Leftrightarrow & \color{red}{2}x & = &-20\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-20}{2} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-12}& = &12 \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12} & = &12\color{blue}{+12} \\\Leftrightarrow &-2x & = &24\\\Leftrightarrow & \color{red}{-2}x & = &24\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{24}{-2} \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-7}& = &13 \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7} & = &13\color{blue}{+7} \\\Leftrightarrow &11x & = &20\\\Leftrightarrow & \color{red}{11}x & = &20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+3}& = &-1 \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3} & = &-1\color{blue}{-3} \\\Leftrightarrow &-9x & = &-4\\\Leftrightarrow & \color{red}{-9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+10}& = &-2 \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10} & = &-2\color{blue}{-10} \\\Leftrightarrow &-9x & = &-12\\\Leftrightarrow & \color{red}{-9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+15}& = &2 \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15} & = &2\color{blue}{-15} \\\Leftrightarrow &-5x & = &-13\\\Leftrightarrow & \color{red}{-5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+5}& = &-13 \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5} & = &-13\color{blue}{-5} \\\Leftrightarrow &15x & = &-18\\\Leftrightarrow & \color{red}{15}x & = &-18\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-18}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-6}& = &-12 \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6} & = &-12\color{blue}{+6} \\\Leftrightarrow &14x & = &-6\\\Leftrightarrow & \color{red}{14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+9}& = &-10 \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9} & = &-10\color{blue}{-9} \\\Leftrightarrow &-5x & = &-19\\\Leftrightarrow & \color{red}{-5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+11}& = &8 \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11} & = &8\color{blue}{-11} \\\Leftrightarrow &15x & = &-3\\\Leftrightarrow & \color{red}{15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-3}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)