Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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