Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & x \color{red}{+13}& = &3 \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13} & = &3\color{blue}{-13} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+6}& = &-12 \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6} & = &-12\color{blue}{-6} \\\Leftrightarrow &4x & = &-18\\\Leftrightarrow & \color{red}{4}x & = &-18\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-18}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+9}& = &-5 \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9} & = &-5\color{blue}{-9} \\\Leftrightarrow &15x & = &-14\\\Leftrightarrow & \color{red}{15}x & = &-14\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-14}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-4}& = &-10 \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4} & = &-10\color{blue}{+4} \\\Leftrightarrow &-4x & = &-6\\\Leftrightarrow & \color{red}{-4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+13}& = &8 \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13} & = &8\color{blue}{-13} \\\Leftrightarrow &9x & = &-5\\\Leftrightarrow & \color{red}{9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+13}& = &-9 \\\Leftrightarrow & -4x \color{red}{+13}\color{blue}{-13} & = &-9\color{blue}{-13} \\\Leftrightarrow &-4x & = &-22\\\Leftrightarrow & \color{red}{-4}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-22}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+12}& = &-6 \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12} & = &-6\color{blue}{-12} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-8}& = &2 \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8} & = &2\color{blue}{+8} \\\Leftrightarrow &14x & = &10\\\Leftrightarrow & \color{red}{14}x & = &10\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{10}{14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+5}& = &5 \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5} & = &5\color{blue}{-5} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-8}& = &-14 \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8} & = &-14\color{blue}{+8} \\\Leftrightarrow &14x & = &-6\\\Leftrightarrow & \color{red}{14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-12}& = &-12 \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12} & = &-12\color{blue}{+12} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+10}& = &-9 \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10} & = &-9\color{blue}{-10} \\\Leftrightarrow &-4x & = &-19\\\Leftrightarrow & \color{red}{-4}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)