Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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