Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+1}& = &14 \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1} & = &14\color{blue}{-1} \\\Leftrightarrow &9x & = &13\\\Leftrightarrow & \color{red}{9}x & = &13\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{13}{9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+2}& = &-2 \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2} & = &-2\color{blue}{-2} \\\Leftrightarrow &-14x & = &-4\\\Leftrightarrow & \color{red}{-14}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-8}& = &15 \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8} & = &15\color{blue}{+8} \\\Leftrightarrow &15x & = &23\\\Leftrightarrow & \color{red}{15}x & = &23\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{23}{15} \\\Leftrightarrow & \color{green}{ x = \frac{23}{15} } & & \\ & V = \left\{ \frac{23}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+2}& = &11 \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2} & = &11\color{blue}{-2} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-6}& = &-9 \\\Leftrightarrow & 6x \color{red}{-6}\color{blue}{+6} & = &-9\color{blue}{+6} \\\Leftrightarrow &6x & = &-3\\\Leftrightarrow & \color{red}{6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+4}& = &-15 \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4} & = &-15\color{blue}{-4} \\\Leftrightarrow &-8x & = &-19\\\Leftrightarrow & \color{red}{-8}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{19}{8} } & & \\ & V = \left\{ \frac{19}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-8}& = &10 \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8} & = &10\color{blue}{+8} \\\Leftrightarrow &-14x & = &18\\\Leftrightarrow & \color{red}{-14}x & = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-13}& = &3 \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13} & = &3\color{blue}{+13} \\\Leftrightarrow &14x & = &16\\\Leftrightarrow & \color{red}{14}x & = &16\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{16}{14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+7}& = &-6 \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7} & = &-6\color{blue}{-7} \\\Leftrightarrow &6x & = &-13\\\Leftrightarrow & \color{red}{6}x & = &-13\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-13}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-14}& = &-5 \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14} & = &-5\color{blue}{+14} \\\Leftrightarrow &-6x & = &9\\\Leftrightarrow & \color{red}{-6}x & = &9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-4}& = &-7 \\\Leftrightarrow & 10x \color{red}{-4}\color{blue}{+4} & = &-7\color{blue}{+4} \\\Leftrightarrow &10x & = &-3\\\Leftrightarrow & \color{red}{10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-15}& = &1 \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15} & = &1\color{blue}{+15} \\\Leftrightarrow &-10x & = &16\\\Leftrightarrow & \color{red}{-10}x & = &16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)