Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-8}& = &12 \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8} & = &12\color{blue}{+8} \\\Leftrightarrow &2x & = &20\\\Leftrightarrow & \color{red}{2}x & = &20\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{20}{2} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+2}& = &9 \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2} & = &9\color{blue}{-2} \\\Leftrightarrow &3x & = &7\\\Leftrightarrow & \color{red}{3}x & = &7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-4}& = &-7 \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4} & = &-7\color{blue}{+4} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-8}& = &7 \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8} & = &7\color{blue}{+8} \\\Leftrightarrow &-3x & = &15\\\Leftrightarrow & \color{red}{-3}x & = &15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{15}{-3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-2}& = &-5 \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2} & = &-5\color{blue}{+2} \\\Leftrightarrow &-15x & = &-3\\\Leftrightarrow & \color{red}{-15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+15}& = &-15 \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15} & = &-15\color{blue}{-15} \\\Leftrightarrow &-14x & = &-30\\\Leftrightarrow & \color{red}{-14}x & = &-30\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-30}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{7} } & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+6}& = &10 \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6} & = &10\color{blue}{-6} \\\Leftrightarrow &-8x & = &4\\\Leftrightarrow & \color{red}{-8}x & = &4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+6}& = &-10 \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6} & = &-10\color{blue}{-6} \\\Leftrightarrow &10x & = &-16\\\Leftrightarrow & \color{red}{10}x & = &-16\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-16}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+3}& = &10 \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3} & = &10\color{blue}{-3} \\\Leftrightarrow &11x & = &7\\\Leftrightarrow & \color{red}{11}x & = &7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-7}& = &-2 \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7} & = &-2\color{blue}{+7} \\\Leftrightarrow &14x & = &5\\\Leftrightarrow & \color{red}{14}x & = &5\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{5}{14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+11}& = &-2 \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11} & = &-2\color{blue}{-11} \\\Leftrightarrow &-12x & = &-13\\\Leftrightarrow & \color{red}{-12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-3}& = &-13 \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3} & = &-13\color{blue}{+3} \\\Leftrightarrow &12x & = &-10\\\Leftrightarrow & \color{red}{12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-10}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)