Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+6}& = &-12 \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6} & = &-12\color{blue}{-6} \\\Leftrightarrow &-5x & = &-18\\\Leftrightarrow & \color{red}{-5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+9}& = &-10 \\\Leftrightarrow & -2x \color{red}{+9}\color{blue}{-9} & = &-10\color{blue}{-9} \\\Leftrightarrow &-2x & = &-19\\\Leftrightarrow & \color{red}{-2}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-19}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{19}{2} } & & \\ & V = \left\{ \frac{19}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+2}& = &9 \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2} & = &9\color{blue}{-2} \\\Leftrightarrow &7x & = &7\\\Leftrightarrow & \color{red}{7}x & = &7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{7}{7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-10}& = &4 \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10} & = &4\color{blue}{+10} \\\Leftrightarrow &-13x & = &14\\\Leftrightarrow & \color{red}{-13}x & = &14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-11}& = &-15 \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11} & = &-15\color{blue}{+11} \\\Leftrightarrow &12x & = &-4\\\Leftrightarrow & \color{red}{12}x & = &-4\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-4}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-15}& = &-11 \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15} & = &-11\color{blue}{+15} \\\Leftrightarrow &-2x & = &4\\\Leftrightarrow & \color{red}{-2}x & = &4\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{4}{-2} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+7}& = &5 \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7} & = &5\color{blue}{-7} \\\Leftrightarrow &-5x & = &-2\\\Leftrightarrow & \color{red}{-5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-10}& = &4 \\\Leftrightarrow & 3x \color{red}{-10}\color{blue}{+10} & = &4\color{blue}{+10} \\\Leftrightarrow &3x & = &14\\\Leftrightarrow & \color{red}{3}x & = &14\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{14}{3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+3}& = &7 \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3} & = &7\color{blue}{-3} \\\Leftrightarrow &6x & = &4\\\Leftrightarrow & \color{red}{6}x & = &4\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{4}{6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-15}& = &3 \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15} & = &3\color{blue}{+15} \\\Leftrightarrow &-6x & = &18\\\Leftrightarrow & \color{red}{-6}x & = &18\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{18}{-6} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-13}& = &-13 \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13} & = &-13\color{blue}{+13} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-13}& = &14 \\\Leftrightarrow & -5x \color{red}{-13}\color{blue}{+13} & = &14\color{blue}{+13} \\\Leftrightarrow &-5x & = &27\\\Leftrightarrow & \color{red}{-5}x & = &27\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{27}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{5} } & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)