Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+13}& = &9 \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13} & = &9\color{blue}{-13} \\\Leftrightarrow &14x & = &-4\\\Leftrightarrow & \color{red}{14}x & = &-4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-6}& = &7 \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6} & = &7\color{blue}{+6} \\\Leftrightarrow &12x & = &13\\\Leftrightarrow & \color{red}{12}x & = &13\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{13}{12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-4}& = &8 \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4} & = &8\color{blue}{+4} \\\Leftrightarrow &6x & = &12\\\Leftrightarrow & \color{red}{6}x & = &12\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{12}{6} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+4}& = &-9 \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4} & = &-9\color{blue}{-4} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-1}& = &6 \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1} & = &6\color{blue}{+1} \\\Leftrightarrow &-15x & = &7\\\Leftrightarrow & \color{red}{-15}x & = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+3}& = &8 \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3} & = &8\color{blue}{-3} \\\Leftrightarrow &6x & = &5\\\Leftrightarrow & \color{red}{6}x & = &5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+9}& = &4 \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9} & = &4\color{blue}{-9} \\\Leftrightarrow &-14x & = &-5\\\Leftrightarrow & \color{red}{-14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+6}& = &-14 \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6} & = &-14\color{blue}{-6} \\\Leftrightarrow &9x & = &-20\\\Leftrightarrow & \color{red}{9}x & = &-20\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-20}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{9} } & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+1}& = &-3 \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1} & = &-3\color{blue}{-1} \\\Leftrightarrow &-13x & = &-4\\\Leftrightarrow & \color{red}{-13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-6}& = &-1 \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6} & = &-1\color{blue}{+6} \\\Leftrightarrow &2x & = &5\\\Leftrightarrow & \color{red}{2}x & = &5\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{5}{2} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-15}& = &-15 \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15} & = &-15\color{blue}{+15} \\\Leftrightarrow &10x & = &0\\\Leftrightarrow & \color{red}{10}x & = &0\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{0}{10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-13}& = &-15 \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13} & = &-15\color{blue}{+13} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)