Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-10}& = &8 \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10} & = &8\color{blue}{+10} \\\Leftrightarrow &10x & = &18\\\Leftrightarrow & \color{red}{10}x & = &18\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{18}{10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-7}& = &-1 \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7} & = &-1\color{blue}{+7} \\\Leftrightarrow &14x & = &6\\\Leftrightarrow & \color{red}{14}x & = &6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-8}& = &12 \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8} & = &12\color{blue}{+8} \\\Leftrightarrow &12x & = &20\\\Leftrightarrow & \color{red}{12}x & = &20\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{20}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-4}& = &12 \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4} & = &12\color{blue}{+4} \\\Leftrightarrow &-11x & = &16\\\Leftrightarrow & \color{red}{-11}x & = &16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-6}& = &-9 \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6} & = &-9\color{blue}{+6} \\\Leftrightarrow &4x & = &-3\\\Leftrightarrow & \color{red}{4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-13}& = &7 \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13} & = &7\color{blue}{+13} \\\Leftrightarrow &12x & = &20\\\Leftrightarrow & \color{red}{12}x & = &20\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{20}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-10}& = &2 \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10} & = &2\color{blue}{+10} \\\Leftrightarrow &5x & = &12\\\Leftrightarrow & \color{red}{5}x & = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+13}& = &2 \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13} & = &2\color{blue}{-13} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-7}& = &7 \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7} & = &7\color{blue}{+7} \\\Leftrightarrow &-11x & = &14\\\Leftrightarrow & \color{red}{-11}x & = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+13}& = &4 \\\Leftrightarrow & -4x \color{red}{+13}\color{blue}{-13} & = &4\color{blue}{-13} \\\Leftrightarrow &-4x & = &-9\\\Leftrightarrow & \color{red}{-4}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-7}& = &1 \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7} & = &1\color{blue}{+7} \\\Leftrightarrow &-x & = &8\\\Leftrightarrow & \color{red}{-}x & = &8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{8}{-1} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-13}& = &-1 \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13} & = &-1\color{blue}{+13} \\\Leftrightarrow &-3x & = &12\\\Leftrightarrow & \color{red}{-3}x & = &12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{12}{-3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)