Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+3}& = &-10 \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3} & = &-10\color{blue}{-3} \\\Leftrightarrow &-6x & = &-13\\\Leftrightarrow & \color{red}{-6}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+6}& = &-1 \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6} & = &-1\color{blue}{-6} \\\Leftrightarrow &-2x & = &-7\\\Leftrightarrow & \color{red}{-2}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-7}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-15}& = &14 \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15} & = &14\color{blue}{+15} \\\Leftrightarrow &-4x & = &29\\\Leftrightarrow & \color{red}{-4}x & = &29\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{29}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{4} } & & \\ & V = \left\{ \frac{-29}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-1}& = &-1 \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1} & = &-1\color{blue}{+1} \\\Leftrightarrow &-12x & = &0\\\Leftrightarrow & \color{red}{-12}x & = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+12}& = &-13 \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12} & = &-13\color{blue}{-12} \\\Leftrightarrow &12x & = &-25\\\Leftrightarrow & \color{red}{12}x & = &-25\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-25}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{12} } & & \\ & V = \left\{ \frac{-25}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+8}& = &-1 \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8} & = &-1\color{blue}{-8} \\\Leftrightarrow &7x & = &-9\\\Leftrightarrow & \color{red}{7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-10}& = &9 \\\Leftrightarrow & -4x \color{red}{-10}\color{blue}{+10} & = &9\color{blue}{+10} \\\Leftrightarrow &-4x & = &19\\\Leftrightarrow & \color{red}{-4}x & = &19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{4} } & & \\ & V = \left\{ \frac{-19}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-14}& = &2 \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14} & = &2\color{blue}{+14} \\\Leftrightarrow &2x & = &16\\\Leftrightarrow & \color{red}{2}x & = &16\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{16}{2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-13}& = &7 \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13} & = &7\color{blue}{+13} \\\Leftrightarrow &6x & = &20\\\Leftrightarrow & \color{red}{6}x & = &20\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{20}{6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-7}& = &-10 \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7} & = &-10\color{blue}{+7} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-2}& = &2 \\\Leftrightarrow & -13x \color{red}{-2}\color{blue}{+2} & = &2\color{blue}{+2} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+13}& = &8 \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13} & = &8\color{blue}{-13} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)