Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-2}& = &-8 \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2} & = &-8\color{blue}{+2} \\\Leftrightarrow &14x & = &-6\\\Leftrightarrow & \color{red}{14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+3}& = &6 \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3} & = &6\color{blue}{-3} \\\Leftrightarrow &-3x & = &3\\\Leftrightarrow & \color{red}{-3}x & = &3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{3}{-3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+12}& = &3 \\\Leftrightarrow & -7x \color{red}{+12}\color{blue}{-12} & = &3\color{blue}{-12} \\\Leftrightarrow &-7x & = &-9\\\Leftrightarrow & \color{red}{-7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+12}& = &-4 \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12} & = &-4\color{blue}{-12} \\\Leftrightarrow &-11x & = &-16\\\Leftrightarrow & \color{red}{-11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+4}& = &-14 \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4} & = &-14\color{blue}{-4} \\\Leftrightarrow &-7x & = &-18\\\Leftrightarrow & \color{red}{-7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-2}& = &5 \\\Leftrightarrow & x \color{red}{-2}\color{blue}{+2} & = &5\color{blue}{+2} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+4}& = &5 \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4} & = &5\color{blue}{-4} \\\Leftrightarrow &-9x & = &1\\\Leftrightarrow & \color{red}{-9}x & = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+6}& = &14 \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6} & = &14\color{blue}{-6} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-14}& = &-5 \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14} & = &-5\color{blue}{+14} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-14}& = &-3 \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14} & = &-3\color{blue}{+14} \\\Leftrightarrow &10x & = &11\\\Leftrightarrow & \color{red}{10}x & = &11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-15}& = &12 \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15} & = &12\color{blue}{+15} \\\Leftrightarrow &-4x & = &27\\\Leftrightarrow & \color{red}{-4}x & = &27\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{27}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{4} } & & \\ & V = \left\{ \frac{-27}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+2}& = &-13 \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2} & = &-13\color{blue}{-2} \\\Leftrightarrow &5x & = &-15\\\Leftrightarrow & \color{red}{5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)