Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-13}& = &12 \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13} & = &12\color{blue}{+13} \\\Leftrightarrow &6x & = &25\\\Leftrightarrow & \color{red}{6}x & = &25\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{25}{6} \\\Leftrightarrow & \color{green}{ x = \frac{25}{6} } & & \\ & V = \left\{ \frac{25}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-4}& = &9 \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4} & = &9\color{blue}{+4} \\\Leftrightarrow &15x & = &13\\\Leftrightarrow & \color{red}{15}x & = &13\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{13}{15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+4}& = &14 \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4} & = &14\color{blue}{-4} \\\Leftrightarrow &2x & = &10\\\Leftrightarrow & \color{red}{2}x & = &10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{10}{2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+5}& = &7 \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5} & = &7\color{blue}{-5} \\\Leftrightarrow &14x & = &2\\\Leftrightarrow & \color{red}{14}x & = &2\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{2}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-6}& = &13 \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6} & = &13\color{blue}{+6} \\\Leftrightarrow &-15x & = &19\\\Leftrightarrow & \color{red}{-15}x & = &19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{15} } & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+7}& = &8 \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7} & = &8\color{blue}{-7} \\\Leftrightarrow &-6x & = &1\\\Leftrightarrow & \color{red}{-6}x & = &1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+1}& = &1 \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1} & = &1\color{blue}{-1} \\\Leftrightarrow &-12x & = &0\\\Leftrightarrow & \color{red}{-12}x & = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-13}& = &13 \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13} & = &13\color{blue}{+13} \\\Leftrightarrow &6x & = &26\\\Leftrightarrow & \color{red}{6}x & = &26\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{26}{6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+12}& = &-2 \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12} & = &-2\color{blue}{-12} \\\Leftrightarrow &8x & = &-14\\\Leftrightarrow & \color{red}{8}x & = &-14\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-14}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-13}& = &10 \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13} & = &10\color{blue}{+13} \\\Leftrightarrow &-3x & = &23\\\Leftrightarrow & \color{red}{-3}x & = &23\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{23}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{3} } & & \\ & V = \left\{ \frac{-23}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-11}& = &-11 \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11} & = &-11\color{blue}{+11} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+3}& = &8 \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3} & = &8\color{blue}{-3} \\\Leftrightarrow &-6x & = &5\\\Leftrightarrow & \color{red}{-6}x & = &5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)