Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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