Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+7}& = &3 \\\Leftrightarrow & -13x \color{red}{+7}\color{blue}{-7} & = &3\color{blue}{-7} \\\Leftrightarrow &-13x & = &-4\\\Leftrightarrow & \color{red}{-13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+1}& = &-6 \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1} & = &-6\color{blue}{-1} \\\Leftrightarrow &15x & = &-7\\\Leftrightarrow & \color{red}{15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-6}& = &-9 \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6} & = &-9\color{blue}{+6} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-5}& = &13 \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5} & = &13\color{blue}{+5} \\\Leftrightarrow &-11x & = &18\\\Leftrightarrow & \color{red}{-11}x & = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-10}& = &9 \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10} & = &9\color{blue}{+10} \\\Leftrightarrow &12x & = &19\\\Leftrightarrow & \color{red}{12}x & = &19\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{19}{12} \\\Leftrightarrow & \color{green}{ x = \frac{19}{12} } & & \\ & V = \left\{ \frac{19}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-8}& = &6 \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8} & = &6\color{blue}{+8} \\\Leftrightarrow &-3x & = &14\\\Leftrightarrow & \color{red}{-3}x & = &14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-5}& = &-15 \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5} & = &-15\color{blue}{+5} \\\Leftrightarrow &12x & = &-10\\\Leftrightarrow & \color{red}{12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-10}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-12}& = &-5 \\\Leftrightarrow & 10x \color{red}{-12}\color{blue}{+12} & = &-5\color{blue}{+12} \\\Leftrightarrow &10x & = &7\\\Leftrightarrow & \color{red}{10}x & = &7\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{7}{10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+15}& = &-2 \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15} & = &-2\color{blue}{-15} \\\Leftrightarrow &-6x & = &-17\\\Leftrightarrow & \color{red}{-6}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+3}& = &12 \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3} & = &12\color{blue}{-3} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-4}& = &-3 \\\Leftrightarrow & -14x \color{red}{-4}\color{blue}{+4} & = &-3\color{blue}{+4} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-13}& = &-14 \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13} & = &-14\color{blue}{+13} \\\Leftrightarrow &2x & = &-1\\\Leftrightarrow & \color{red}{2}x & = &-1\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-1}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)