Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-5}& = &1 \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5} & = &1\color{blue}{+5} \\\Leftrightarrow &-x & = &6\\\Leftrightarrow & \color{red}{-}x & = &6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{6}{-1} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+4}& = &-2 \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4} & = &-2\color{blue}{-4} \\\Leftrightarrow &6x & = &-6\\\Leftrightarrow & \color{red}{6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-6}{6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+4}& = &12 \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4} & = &12\color{blue}{-4} \\\Leftrightarrow &7x & = &8\\\Leftrightarrow & \color{red}{7}x & = &8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+13}& = &-3 \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13} & = &-3\color{blue}{-13} \\\Leftrightarrow &15x & = &-16\\\Leftrightarrow & \color{red}{15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-16}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+15}& = &-8 \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15} & = &-8\color{blue}{-15} \\\Leftrightarrow &4x & = &-23\\\Leftrightarrow & \color{red}{4}x & = &-23\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-23}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{4} } & & \\ & V = \left\{ \frac{-23}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+8}& = &-2 \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8} & = &-2\color{blue}{-8} \\\Leftrightarrow &11x & = &-10\\\Leftrightarrow & \color{red}{11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+12}& = &-1 \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12} & = &-1\color{blue}{-12} \\\Leftrightarrow &3x & = &-13\\\Leftrightarrow & \color{red}{3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+10}& = &3 \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10} & = &3\color{blue}{-10} \\\Leftrightarrow &15x & = &-7\\\Leftrightarrow & \color{red}{15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-14}& = &12 \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14} & = &12\color{blue}{+14} \\\Leftrightarrow &-3x & = &26\\\Leftrightarrow & \color{red}{-3}x & = &26\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{26}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{3} } & & \\ & V = \left\{ \frac{-26}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{-13}& = &8 \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13} & = &8\color{blue}{+13} \\\Leftrightarrow &-15x & = &21\\\Leftrightarrow & \color{red}{-15}x & = &21\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{21}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+4}& = &11 \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4} & = &11\color{blue}{-4} \\\Leftrightarrow &14x & = &7\\\Leftrightarrow & \color{red}{14}x & = &7\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{7}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+5}& = &-9 \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5} & = &-9\color{blue}{-5} \\\Leftrightarrow &5x & = &-14\\\Leftrightarrow & \color{red}{5}x & = &-14\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-14}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{5} } & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)