Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-6}& = &3 \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6} & = &3\color{blue}{+6} \\\Leftrightarrow &8x & = &9\\\Leftrightarrow & \color{red}{8}x & = &9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-14}& = &11 \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14} & = &11\color{blue}{+14} \\\Leftrightarrow &5x & = &25\\\Leftrightarrow & \color{red}{5}x & = &25\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{25}{5} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-1}& = &-14 \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1} & = &-14\color{blue}{+1} \\\Leftrightarrow &-11x & = &-13\\\Leftrightarrow & \color{red}{-11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-10}& = &11 \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10} & = &11\color{blue}{+10} \\\Leftrightarrow &-14x & = &21\\\Leftrightarrow & \color{red}{-14}x & = &21\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{21}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+4}& = &-7 \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4} & = &-7\color{blue}{-4} \\\Leftrightarrow &-6x & = &-11\\\Leftrightarrow & \color{red}{-6}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+14}& = &-7 \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14} & = &-7\color{blue}{-14} \\\Leftrightarrow &-6x & = &-21\\\Leftrightarrow & \color{red}{-6}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-21}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-10}& = &2 \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10} & = &2\color{blue}{+10} \\\Leftrightarrow &14x & = &12\\\Leftrightarrow & \color{red}{14}x & = &12\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{12}{14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+3}& = &-8 \\\Leftrightarrow & -15x \color{red}{+3}\color{blue}{-3} & = &-8\color{blue}{-3} \\\Leftrightarrow &-15x & = &-11\\\Leftrightarrow & \color{red}{-15}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{11}{15} } & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-14}& = &-2 \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14} & = &-2\color{blue}{+14} \\\Leftrightarrow &-11x & = &12\\\Leftrightarrow & \color{red}{-11}x & = &12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{11} } & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+11}& = &-7 \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11} & = &-7\color{blue}{-11} \\\Leftrightarrow &6x & = &-18\\\Leftrightarrow & \color{red}{6}x & = &-18\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-18}{6} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-2}& = &-11 \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2} & = &-11\color{blue}{+2} \\\Leftrightarrow &10x & = &-9\\\Leftrightarrow & \color{red}{10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-9}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-1}& = &14 \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1} & = &14\color{blue}{+1} \\\Leftrightarrow &-3x & = &15\\\Leftrightarrow & \color{red}{-3}x & = &15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{15}{-3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)