Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-12}& = &14 \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12} & = &14\color{blue}{+12} \\\Leftrightarrow &-3x & = &26\\\Leftrightarrow & \color{red}{-3}x & = &26\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{26}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{3} } & & \\ & V = \left\{ \frac{-26}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-9}& = &-6 \\\Leftrightarrow & 6x \color{red}{-9}\color{blue}{+9} & = &-6\color{blue}{+9} \\\Leftrightarrow &6x & = &3\\\Leftrightarrow & \color{red}{6}x & = &3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-13}& = &9 \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13} & = &9\color{blue}{+13} \\\Leftrightarrow &14x & = &22\\\Leftrightarrow & \color{red}{14}x & = &22\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{22}{14} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+10}& = &-2 \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10} & = &-2\color{blue}{-10} \\\Leftrightarrow &2x & = &-12\\\Leftrightarrow & \color{red}{2}x & = &-12\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-12}{2} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+15}& = &8 \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15} & = &8\color{blue}{-15} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-4}& = &-4 \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4} & = &-4\color{blue}{+4} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+12}& = &2 \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12} & = &2\color{blue}{-12} \\\Leftrightarrow &11x & = &-10\\\Leftrightarrow & \color{red}{11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+5}& = &4 \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5} & = &4\color{blue}{-5} \\\Leftrightarrow &14x & = &-1\\\Leftrightarrow & \color{red}{14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-14}& = &4 \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14} & = &4\color{blue}{+14} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+11}& = &-12 \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11} & = &-12\color{blue}{-11} \\\Leftrightarrow &-13x & = &-23\\\Leftrightarrow & \color{red}{-13}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-23}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{23}{13} } & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+9}& = &12 \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9} & = &12\color{blue}{-9} \\\Leftrightarrow &13x & = &3\\\Leftrightarrow & \color{red}{13}x & = &3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+15}& = &-14 \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15} & = &-14\color{blue}{-15} \\\Leftrightarrow &-7x & = &-29\\\Leftrightarrow & \color{red}{-7}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-29}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{29}{7} } & & \\ & V = \left\{ \frac{29}{7} \right\} & \\\end{align}\)