Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+6}& = &-12 \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6} & = &-12\color{blue}{-6} \\\Leftrightarrow &-3x & = &-18\\\Leftrightarrow & \color{red}{-3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-18}{-3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+14}& = &-8 \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14} & = &-8\color{blue}{-14} \\\Leftrightarrow &-7x & = &-22\\\Leftrightarrow & \color{red}{-7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{22}{7} } & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-2}& = &-15 \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2} & = &-15\color{blue}{+2} \\\Leftrightarrow &6x & = &-13\\\Leftrightarrow & \color{red}{6}x & = &-13\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-13}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+10}& = &-8 \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10} & = &-8\color{blue}{-10} \\\Leftrightarrow &-12x & = &-18\\\Leftrightarrow & \color{red}{-12}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-18}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+5}& = &3 \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5} & = &3\color{blue}{-5} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-14}& = &-8 \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14} & = &-8\color{blue}{+14} \\\Leftrightarrow &-12x & = &6\\\Leftrightarrow & \color{red}{-12}x & = &6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-10}& = &14 \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10} & = &14\color{blue}{+10} \\\Leftrightarrow &-10x & = &24\\\Leftrightarrow & \color{red}{-10}x & = &24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+5}& = &-11 \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5} & = &-11\color{blue}{-5} \\\Leftrightarrow &-10x & = &-16\\\Leftrightarrow & \color{red}{-10}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{+5}& = &14 \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5} & = &14\color{blue}{-5} \\\Leftrightarrow &-14x & = &9\\\Leftrightarrow & \color{red}{-14}x & = &9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-9}& = &-14 \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9} & = &-14\color{blue}{+9} \\\Leftrightarrow &14x & = &-5\\\Leftrightarrow & \color{red}{14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-5}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+15}& = &-5 \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15} & = &-5\color{blue}{-15} \\\Leftrightarrow &14x & = &-20\\\Leftrightarrow & \color{red}{14}x & = &-20\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-20}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-6}& = &7 \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6} & = &7\color{blue}{+6} \\\Leftrightarrow &-6x & = &13\\\Leftrightarrow & \color{red}{-6}x & = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)