Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+7}& = &-12 \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7} & = &-12\color{blue}{-7} \\\Leftrightarrow &14x & = &-19\\\Leftrightarrow & \color{red}{14}x & = &-19\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-19}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{14} } & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-4}& = &3 \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4} & = &3\color{blue}{+4} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-12}& = &13 \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12} & = &13\color{blue}{+12} \\\Leftrightarrow &12x & = &25\\\Leftrightarrow & \color{red}{12}x & = &25\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{25}{12} \\\Leftrightarrow & \color{green}{ x = \frac{25}{12} } & & \\ & V = \left\{ \frac{25}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+5}& = &7 \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5} & = &7\color{blue}{-5} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-6}& = &-8 \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6} & = &-8\color{blue}{+6} \\\Leftrightarrow &9x & = &-2\\\Leftrightarrow & \color{red}{9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+5}& = &3 \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5} & = &3\color{blue}{-5} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+4}& = &-13 \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4} & = &-13\color{blue}{-4} \\\Leftrightarrow &2x & = &-17\\\Leftrightarrow & \color{red}{2}x & = &-17\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-17}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{2} } & & \\ & V = \left\{ \frac{-17}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+5}& = &1 \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5} & = &1\color{blue}{-5} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-4}& = &-13 \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4} & = &-13\color{blue}{+4} \\\Leftrightarrow &8x & = &-9\\\Leftrightarrow & \color{red}{8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+4}& = &-15 \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4} & = &-15\color{blue}{-4} \\\Leftrightarrow &x & = &-19\\\Leftrightarrow & \color{red}{}x & = &-19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -19 \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{-5}& = &1 \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5} & = &1\color{blue}{+5} \\\Leftrightarrow &12x & = &6\\\Leftrightarrow & \color{red}{12}x & = &6\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{6}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+13}& = &-15 \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13} & = &-15\color{blue}{-13} \\\Leftrightarrow &4x & = &-28\\\Leftrightarrow & \color{red}{4}x & = &-28\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-28}{4} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)