Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{-13}& = &-8 \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13} & = &-8\color{blue}{+13} \\\Leftrightarrow &-14x & = &5\\\Leftrightarrow & \color{red}{-14}x & = &5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-5}& = &-10 \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5} & = &-10\color{blue}{+5} \\\Leftrightarrow &6x & = &-5\\\Leftrightarrow & \color{red}{6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+12}& = &-10 \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12} & = &-10\color{blue}{-12} \\\Leftrightarrow &6x & = &-22\\\Leftrightarrow & \color{red}{6}x & = &-22\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-22}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-6}& = &5 \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6} & = &5\color{blue}{+6} \\\Leftrightarrow &-5x & = &11\\\Leftrightarrow & \color{red}{-5}x & = &11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+7}& = &12 \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7} & = &12\color{blue}{-7} \\\Leftrightarrow &6x & = &5\\\Leftrightarrow & \color{red}{6}x & = &5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+8}& = &-13 \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8} & = &-13\color{blue}{-8} \\\Leftrightarrow &14x & = &-21\\\Leftrightarrow & \color{red}{14}x & = &-21\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-21}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-12}& = &10 \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12} & = &10\color{blue}{+12} \\\Leftrightarrow &-5x & = &22\\\Leftrightarrow & \color{red}{-5}x & = &22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{5} } & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-7}& = &-12 \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7} & = &-12\color{blue}{+7} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+8}& = &-15 \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8} & = &-15\color{blue}{-8} \\\Leftrightarrow &8x & = &-23\\\Leftrightarrow & \color{red}{8}x & = &-23\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-23}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{8} } & & \\ & V = \left\{ \frac{-23}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-12}& = &-13 \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12} & = &-13\color{blue}{+12} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+3}& = &9 \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3} & = &9\color{blue}{-3} \\\Leftrightarrow &3x & = &6\\\Leftrightarrow & \color{red}{3}x & = &6\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{6}{3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-7}& = &-13 \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7} & = &-13\color{blue}{+7} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)