Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+15}& = &3 \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15} & = &3\color{blue}{-15} \\\Leftrightarrow &6x & = &-12\\\Leftrightarrow & \color{red}{6}x & = &-12\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-12}{6} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-5}& = &-10 \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5} & = &-10\color{blue}{+5} \\\Leftrightarrow &-13x & = &-5\\\Leftrightarrow & \color{red}{-13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+3}& = &-6 \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3} & = &-6\color{blue}{-3} \\\Leftrightarrow &9x & = &-9\\\Leftrightarrow & \color{red}{9}x & = &-9\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-9}{9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-1}& = &7 \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1} & = &7\color{blue}{+1} \\\Leftrightarrow &-15x & = &8\\\Leftrightarrow & \color{red}{-15}x & = &8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+1}& = &-7 \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1} & = &-7\color{blue}{-1} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+4}& = &-15 \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4} & = &-15\color{blue}{-4} \\\Leftrightarrow &-x & = &-19\\\Leftrightarrow & \color{red}{-}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-19}{-1} \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-13}& = &-7 \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13} & = &-7\color{blue}{+13} \\\Leftrightarrow &-7x & = &6\\\Leftrightarrow & \color{red}{-7}x & = &6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-12}& = &-3 \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12} & = &-3\color{blue}{+12} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-14}& = &11 \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14} & = &11\color{blue}{+14} \\\Leftrightarrow &4x & = &25\\\Leftrightarrow & \color{red}{4}x & = &25\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{25}{4} \\\Leftrightarrow & \color{green}{ x = \frac{25}{4} } & & \\ & V = \left\{ \frac{25}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-11}& = &-7 \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11} & = &-7\color{blue}{+11} \\\Leftrightarrow &-5x & = &4\\\Leftrightarrow & \color{red}{-5}x & = &4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+10}& = &12 \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10} & = &12\color{blue}{-10} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+6}& = &-15 \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6} & = &-15\color{blue}{-6} \\\Leftrightarrow &x & = &-21\\\Leftrightarrow & \color{red}{}x & = &-21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -21 \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)