Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+5}& = &-8 \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5} & = &-8\color{blue}{-5} \\\Leftrightarrow &10x & = &-13\\\Leftrightarrow & \color{red}{10}x & = &-13\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-13}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-13}& = &6 \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13} & = &6\color{blue}{+13} \\\Leftrightarrow &-12x & = &19\\\Leftrightarrow & \color{red}{-12}x & = &19\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{19}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{12} } & & \\ & V = \left\{ \frac{-19}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+8}& = &-13 \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8} & = &-13\color{blue}{-8} \\\Leftrightarrow &14x & = &-21\\\Leftrightarrow & \color{red}{14}x & = &-21\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-21}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+7}& = &-2 \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7} & = &-2\color{blue}{-7} \\\Leftrightarrow &5x & = &-9\\\Leftrightarrow & \color{red}{5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-10}& = &10 \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10} & = &10\color{blue}{+10} \\\Leftrightarrow &7x & = &20\\\Leftrightarrow & \color{red}{7}x & = &20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{20}{7} } & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+10}& = &-11 \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10} & = &-11\color{blue}{-10} \\\Leftrightarrow &-6x & = &-21\\\Leftrightarrow & \color{red}{-6}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-21}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+1}& = &-4 \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1} & = &-4\color{blue}{-1} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-15}& = &-13 \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15} & = &-13\color{blue}{+15} \\\Leftrightarrow &15x & = &2\\\Leftrightarrow & \color{red}{15}x & = &2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+13}& = &6 \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13} & = &6\color{blue}{-13} \\\Leftrightarrow &8x & = &-7\\\Leftrightarrow & \color{red}{8}x & = &-7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+3}& = &9 \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3} & = &9\color{blue}{-3} \\\Leftrightarrow &9x & = &6\\\Leftrightarrow & \color{red}{9}x & = &6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-6}& = &-8 \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6} & = &-8\color{blue}{+6} \\\Leftrightarrow &14x & = &-2\\\Leftrightarrow & \color{red}{14}x & = &-2\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-2}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-14}& = &-3 \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14} & = &-3\color{blue}{+14} \\\Leftrightarrow &7x & = &11\\\Leftrightarrow & \color{red}{7}x & = &11\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{11}{7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)