Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & x \color{red}{-14}& = &1 \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14} & = &1\color{blue}{+14} \\\Leftrightarrow &x & = &15\\\Leftrightarrow & \color{red}{}x & = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-11}& = &13 \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11} & = &13\color{blue}{+11} \\\Leftrightarrow &-3x & = &24\\\Leftrightarrow & \color{red}{-3}x & = &24\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{24}{-3} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-8}& = &6 \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8} & = &6\color{blue}{+8} \\\Leftrightarrow &-13x & = &14\\\Leftrightarrow & \color{red}{-13}x & = &14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-5}& = &-9 \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5} & = &-9\color{blue}{+5} \\\Leftrightarrow &9x & = &-4\\\Leftrightarrow & \color{red}{9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+2}& = &-5 \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2} & = &-5\color{blue}{-2} \\\Leftrightarrow &6x & = &-7\\\Leftrightarrow & \color{red}{6}x & = &-7\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-7}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-7}& = &-2 \\\Leftrightarrow & -5x \color{red}{-7}\color{blue}{+7} & = &-2\color{blue}{+7} \\\Leftrightarrow &-5x & = &5\\\Leftrightarrow & \color{red}{-5}x & = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-15}& = &11 \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15} & = &11\color{blue}{+15} \\\Leftrightarrow &-11x & = &26\\\Leftrightarrow & \color{red}{-11}x & = &26\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{26}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{11} } & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-14}& = &12 \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14} & = &12\color{blue}{+14} \\\Leftrightarrow &-12x & = &26\\\Leftrightarrow & \color{red}{-12}x & = &26\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{26}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+3}& = &-5 \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3} & = &-5\color{blue}{-3} \\\Leftrightarrow &15x & = &-8\\\Leftrightarrow & \color{red}{15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-8}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+3}& = &-13 \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3} & = &-13\color{blue}{-3} \\\Leftrightarrow &-14x & = &-16\\\Leftrightarrow & \color{red}{-14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-14}& = &-1 \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14} & = &-1\color{blue}{+14} \\\Leftrightarrow &-4x & = &13\\\Leftrightarrow & \color{red}{-4}x & = &13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{4} } & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-9}& = &-10 \\\Leftrightarrow & 2x \color{red}{-9}\color{blue}{+9} & = &-10\color{blue}{+9} \\\Leftrightarrow &2x & = &-1\\\Leftrightarrow & \color{red}{2}x & = &-1\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-1}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)