Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-6}& = &-4 \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6} & = &-4\color{blue}{+6} \\\Leftrightarrow &-12x & = &2\\\Leftrightarrow & \color{red}{-12}x & = &2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-4}& = &-11 \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4} & = &-11\color{blue}{+4} \\\Leftrightarrow &-10x & = &-7\\\Leftrightarrow & \color{red}{-10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+5}& = &-6 \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5} & = &-6\color{blue}{-5} \\\Leftrightarrow &6x & = &-11\\\Leftrightarrow & \color{red}{6}x & = &-11\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-11}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-3}& = &6 \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3} & = &6\color{blue}{+3} \\\Leftrightarrow &6x & = &9\\\Leftrightarrow & \color{red}{6}x & = &9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+1}& = &10 \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1} & = &10\color{blue}{-1} \\\Leftrightarrow &5x & = &9\\\Leftrightarrow & \color{red}{5}x & = &9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+2}& = &-6 \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2} & = &-6\color{blue}{-2} \\\Leftrightarrow &4x & = &-8\\\Leftrightarrow & \color{red}{4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-8}{4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-9}& = &-1 \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9} & = &-1\color{blue}{+9} \\\Leftrightarrow &-3x & = &8\\\Leftrightarrow & \color{red}{-3}x & = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-8}& = &-12 \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8} & = &-12\color{blue}{+8} \\\Leftrightarrow &-7x & = &-4\\\Leftrightarrow & \color{red}{-7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-12}& = &14 \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12} & = &14\color{blue}{+12} \\\Leftrightarrow &5x & = &26\\\Leftrightarrow & \color{red}{5}x & = &26\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{26}{5} \\\Leftrightarrow & \color{green}{ x = \frac{26}{5} } & & \\ & V = \left\{ \frac{26}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+11}& = &-13 \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11} & = &-13\color{blue}{-11} \\\Leftrightarrow &-x & = &-24\\\Leftrightarrow & \color{red}{-}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-24}{-1} \\\Leftrightarrow & \color{green}{ x = 24 } & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+9}& = &7 \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9} & = &7\color{blue}{-9} \\\Leftrightarrow &-10x & = &-2\\\Leftrightarrow & \color{red}{-10}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-13}& = &1 \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13} & = &1\color{blue}{+13} \\\Leftrightarrow &-9x & = &14\\\Leftrightarrow & \color{red}{-9}x & = &14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)