Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+14}& = &-4 \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14} & = &-4\color{blue}{-14} \\\Leftrightarrow &14x & = &-18\\\Leftrightarrow & \color{red}{14}x & = &-18\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-18}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+10}& = &-10 \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10} & = &-10\color{blue}{-10} \\\Leftrightarrow &-12x & = &-20\\\Leftrightarrow & \color{red}{-12}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-20}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+4}& = &8 \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4} & = &8\color{blue}{-4} \\\Leftrightarrow &-4x & = &4\\\Leftrightarrow & \color{red}{-4}x & = &4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{4}{-4} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{+12}& = &4 \\\Leftrightarrow & x \color{red}{+12}\color{blue}{-12} & = &4\color{blue}{-12} \\\Leftrightarrow &x & = &-8\\\Leftrightarrow & \color{red}{}x & = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-3}& = &-8 \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3} & = &-8\color{blue}{+3} \\\Leftrightarrow &6x & = &-5\\\Leftrightarrow & \color{red}{6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-12}& = &-3 \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12} & = &-3\color{blue}{+12} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+15}& = &-4 \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15} & = &-4\color{blue}{-15} \\\Leftrightarrow &-2x & = &-19\\\Leftrightarrow & \color{red}{-2}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-19}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{19}{2} } & & \\ & V = \left\{ \frac{19}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+6}& = &4 \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6} & = &4\color{blue}{-6} \\\Leftrightarrow &6x & = &-2\\\Leftrightarrow & \color{red}{6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-2}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+5}& = &-7 \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5} & = &-7\color{blue}{-5} \\\Leftrightarrow &10x & = &-12\\\Leftrightarrow & \color{red}{10}x & = &-12\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-12}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+10}& = &13 \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10} & = &13\color{blue}{-10} \\\Leftrightarrow &-12x & = &3\\\Leftrightarrow & \color{red}{-12}x & = &3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+8}& = &10 \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8} & = &10\color{blue}{-8} \\\Leftrightarrow &-15x & = &2\\\Leftrightarrow & \color{red}{-15}x & = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+15}& = &-4 \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15} & = &-4\color{blue}{-15} \\\Leftrightarrow &9x & = &-19\\\Leftrightarrow & \color{red}{9}x & = &-19\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-19}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)