Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+12}& = &-2 \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12} & = &-2\color{blue}{-12} \\\Leftrightarrow &-4x & = &-14\\\Leftrightarrow & \color{red}{-4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-14}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-15}& = &7 \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15} & = &7\color{blue}{+15} \\\Leftrightarrow &6x & = &22\\\Leftrightarrow & \color{red}{6}x & = &22\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{22}{6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+11}& = &10 \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11} & = &10\color{blue}{-11} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+1}& = &7 \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1} & = &7\color{blue}{-1} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-6}& = &10 \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6} & = &10\color{blue}{+6} \\\Leftrightarrow &-15x & = &16\\\Leftrightarrow & \color{red}{-15}x & = &16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-6}& = &-6 \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6} & = &-6\color{blue}{+6} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+1}& = &-11 \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1} & = &-11\color{blue}{-1} \\\Leftrightarrow &14x & = &-12\\\Leftrightarrow & \color{red}{14}x & = &-12\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-12}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-5}& = &14 \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5} & = &14\color{blue}{+5} \\\Leftrightarrow &3x & = &19\\\Leftrightarrow & \color{red}{3}x & = &19\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{19}{3} \\\Leftrightarrow & \color{green}{ x = \frac{19}{3} } & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+14}& = &-13 \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14} & = &-13\color{blue}{-14} \\\Leftrightarrow &-2x & = &-27\\\Leftrightarrow & \color{red}{-2}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-27}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{27}{2} } & & \\ & V = \left\{ \frac{27}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+7}& = &2 \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7} & = &2\color{blue}{-7} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-5}& = &-8 \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5} & = &-8\color{blue}{+5} \\\Leftrightarrow &4x & = &-3\\\Leftrightarrow & \color{red}{4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+2}& = &-7 \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2} & = &-7\color{blue}{-2} \\\Leftrightarrow &-14x & = &-9\\\Leftrightarrow & \color{red}{-14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)