Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & x \color{red}{-6}& = &-1 \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6} & = &-1\color{blue}{+6} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-11}& = &14 \\\Leftrightarrow & 6x \color{red}{-11}\color{blue}{+11} & = &14\color{blue}{+11} \\\Leftrightarrow &6x & = &25\\\Leftrightarrow & \color{red}{6}x & = &25\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{25}{6} \\\Leftrightarrow & \color{green}{ x = \frac{25}{6} } & & \\ & V = \left\{ \frac{25}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+10}& = &-14 \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10} & = &-14\color{blue}{-10} \\\Leftrightarrow &x & = &-24\\\Leftrightarrow & \color{red}{}x & = &-24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -24 \\\Leftrightarrow & \color{green}{ x = -24 } & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-10}& = &5 \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10} & = &5\color{blue}{+10} \\\Leftrightarrow &8x & = &15\\\Leftrightarrow & \color{red}{8}x & = &15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+12}& = &-7 \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12} & = &-7\color{blue}{-12} \\\Leftrightarrow &2x & = &-19\\\Leftrightarrow & \color{red}{2}x & = &-19\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-19}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{2} } & & \\ & V = \left\{ \frac{-19}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+9}& = &12 \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9} & = &12\color{blue}{-9} \\\Leftrightarrow &14x & = &3\\\Leftrightarrow & \color{red}{14}x & = &3\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{3}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+14}& = &-4 \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14} & = &-4\color{blue}{-14} \\\Leftrightarrow &5x & = &-18\\\Leftrightarrow & \color{red}{5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-1}& = &9 \\\Leftrightarrow & 10x \color{red}{-1}\color{blue}{+1} & = &9\color{blue}{+1} \\\Leftrightarrow &10x & = &10\\\Leftrightarrow & \color{red}{10}x & = &10\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{10}{10} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-6}& = &13 \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6} & = &13\color{blue}{+6} \\\Leftrightarrow &8x & = &19\\\Leftrightarrow & \color{red}{8}x & = &19\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{19}{8} \\\Leftrightarrow & \color{green}{ x = \frac{19}{8} } & & \\ & V = \left\{ \frac{19}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-13}& = &-3 \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13} & = &-3\color{blue}{+13} \\\Leftrightarrow &14x & = &10\\\Leftrightarrow & \color{red}{14}x & = &10\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{10}{14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-1}& = &5 \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1} & = &5\color{blue}{+1} \\\Leftrightarrow &2x & = &6\\\Leftrightarrow & \color{red}{2}x & = &6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{6}{2} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+11}& = &-4 \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11} & = &-4\color{blue}{-11} \\\Leftrightarrow &15x & = &-15\\\Leftrightarrow & \color{red}{15}x & = &-15\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-15}{15} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)