Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-12}& = &-8 \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12} & = &-8\color{blue}{+12} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-12}& = &13 \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12} & = &13\color{blue}{+12} \\\Leftrightarrow &-7x & = &25\\\Leftrightarrow & \color{red}{-7}x & = &25\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{25}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{7} } & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-12}& = &-3 \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12} & = &-3\color{blue}{+12} \\\Leftrightarrow &12x & = &9\\\Leftrightarrow & \color{red}{12}x & = &9\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{9}{12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+12}& = &-13 \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12} & = &-13\color{blue}{-12} \\\Leftrightarrow &-6x & = &-25\\\Leftrightarrow & \color{red}{-6}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-25}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{25}{6} } & & \\ & V = \left\{ \frac{25}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-13}& = &5 \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13} & = &5\color{blue}{+13} \\\Leftrightarrow &12x & = &18\\\Leftrightarrow & \color{red}{12}x & = &18\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{18}{12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+9}& = &10 \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9} & = &10\color{blue}{-9} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+13}& = &12 \\\Leftrightarrow & 7x \color{red}{+13}\color{blue}{-13} & = &12\color{blue}{-13} \\\Leftrightarrow &7x & = &-1\\\Leftrightarrow & \color{red}{7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-5}& = &-13 \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5} & = &-13\color{blue}{+5} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-5}& = &15 \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5} & = &15\color{blue}{+5} \\\Leftrightarrow &12x & = &20\\\Leftrightarrow & \color{red}{12}x & = &20\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{20}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-7}& = &-3 \\\Leftrightarrow & -8x \color{red}{-7}\color{blue}{+7} & = &-3\color{blue}{+7} \\\Leftrightarrow &-8x & = &4\\\Leftrightarrow & \color{red}{-8}x & = &4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-6}& = &1 \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6} & = &1\color{blue}{+6} \\\Leftrightarrow &7x & = &7\\\Leftrightarrow & \color{red}{7}x & = &7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{7}{7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-2}& = &-4 \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2} & = &-4\color{blue}{+2} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)