Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & x \color{red}{-10}& = &-1 \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10} & = &-1\color{blue}{+10} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+4}& = &-4 \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4} & = &-4\color{blue}{-4} \\\Leftrightarrow &-6x & = &-8\\\Leftrightarrow & \color{red}{-6}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-15}& = &7 \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15} & = &7\color{blue}{+15} \\\Leftrightarrow &13x & = &22\\\Leftrightarrow & \color{red}{13}x & = &22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+14}& = &-6 \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14} & = &-6\color{blue}{-14} \\\Leftrightarrow &15x & = &-20\\\Leftrightarrow & \color{red}{15}x & = &-20\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-20}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+2}& = &-5 \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2} & = &-5\color{blue}{-2} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-5}& = &-9 \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5} & = &-9\color{blue}{+5} \\\Leftrightarrow &6x & = &-4\\\Leftrightarrow & \color{red}{6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-4}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-3}& = &6 \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3} & = &6\color{blue}{+3} \\\Leftrightarrow &-8x & = &9\\\Leftrightarrow & \color{red}{-8}x & = &9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+15}& = &-4 \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15} & = &-4\color{blue}{-15} \\\Leftrightarrow &10x & = &-19\\\Leftrightarrow & \color{red}{10}x & = &-19\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-19}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{10} } & & \\ & V = \left\{ \frac{-19}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+15}& = &10 \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15} & = &10\color{blue}{-15} \\\Leftrightarrow &-10x & = &-5\\\Leftrightarrow & \color{red}{-10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-5}& = &3 \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5} & = &3\color{blue}{+5} \\\Leftrightarrow &5x & = &8\\\Leftrightarrow & \color{red}{5}x & = &8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+5}& = &-10 \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5} & = &-10\color{blue}{-5} \\\Leftrightarrow &-3x & = &-15\\\Leftrightarrow & \color{red}{-3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-15}{-3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+5}& = &-5 \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5} & = &-5\color{blue}{-5} \\\Leftrightarrow &6x & = &-10\\\Leftrightarrow & \color{red}{6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-10}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)