Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-9}& = &9 \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9} & = &9\color{blue}{+9} \\\Leftrightarrow &-10x & = &18\\\Leftrightarrow & \color{red}{-10}x & = &18\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{18}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+14}& = &-6 \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14} & = &-6\color{blue}{-14} \\\Leftrightarrow &-2x & = &-20\\\Leftrightarrow & \color{red}{-2}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-20}{-2} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-8}& = &-10 \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8} & = &-10\color{blue}{+8} \\\Leftrightarrow &9x & = &-2\\\Leftrightarrow & \color{red}{9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-13}& = &-2 \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13} & = &-2\color{blue}{+13} \\\Leftrightarrow &-11x & = &11\\\Leftrightarrow & \color{red}{-11}x & = &11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{11}{-11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+9}& = &-13 \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9} & = &-13\color{blue}{-9} \\\Leftrightarrow &-13x & = &-22\\\Leftrightarrow & \color{red}{-13}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+5}& = &-2 \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5} & = &-2\color{blue}{-5} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+13}& = &-14 \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13} & = &-14\color{blue}{-13} \\\Leftrightarrow &15x & = &-27\\\Leftrightarrow & \color{red}{15}x & = &-27\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-27}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-15}& = &15 \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15} & = &15\color{blue}{+15} \\\Leftrightarrow &6x & = &30\\\Leftrightarrow & \color{red}{6}x & = &30\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{30}{6} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-5}& = &-7 \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5} & = &-7\color{blue}{+5} \\\Leftrightarrow &12x & = &-2\\\Leftrightarrow & \color{red}{12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-2}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-4}& = &-13 \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4} & = &-13\color{blue}{+4} \\\Leftrightarrow &-5x & = &-9\\\Leftrightarrow & \color{red}{-5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+11}& = &-2 \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11} & = &-2\color{blue}{-11} \\\Leftrightarrow &-13x & = &-13\\\Leftrightarrow & \color{red}{-13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+7}& = &-6 \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7} & = &-6\color{blue}{-7} \\\Leftrightarrow &-6x & = &-13\\\Leftrightarrow & \color{red}{-6}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)