Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-9}& = &-2 \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9} & = &-2\color{blue}{+9} \\\Leftrightarrow &-8x & = &7\\\Leftrightarrow & \color{red}{-8}x & = &7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+9}& = &2 \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9} & = &2\color{blue}{-9} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+5}& = &-8 \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5} & = &-8\color{blue}{-5} \\\Leftrightarrow &-15x & = &-13\\\Leftrightarrow & \color{red}{-15}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+15}& = &-7 \\\Leftrightarrow & 3x \color{red}{+15}\color{blue}{-15} & = &-7\color{blue}{-15} \\\Leftrightarrow &3x & = &-22\\\Leftrightarrow & \color{red}{3}x & = &-22\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-22}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{3} } & & \\ & V = \left\{ \frac{-22}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+14}& = &-14 \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14} & = &-14\color{blue}{-14} \\\Leftrightarrow &-9x & = &-28\\\Leftrightarrow & \color{red}{-9}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-28}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{28}{9} } & & \\ & V = \left\{ \frac{28}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-3}& = &13 \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3} & = &13\color{blue}{+3} \\\Leftrightarrow &-10x & = &16\\\Leftrightarrow & \color{red}{-10}x & = &16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-1}& = &6 \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1} & = &6\color{blue}{+1} \\\Leftrightarrow &12x & = &7\\\Leftrightarrow & \color{red}{12}x & = &7\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{7}{12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+8}& = &-14 \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8} & = &-14\color{blue}{-8} \\\Leftrightarrow &3x & = &-22\\\Leftrightarrow & \color{red}{3}x & = &-22\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-22}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{3} } & & \\ & V = \left\{ \frac{-22}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+12}& = &15 \\\Leftrightarrow & -12x \color{red}{+12}\color{blue}{-12} & = &15\color{blue}{-12} \\\Leftrightarrow &-12x & = &3\\\Leftrightarrow & \color{red}{-12}x & = &3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+12}& = &7 \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12} & = &7\color{blue}{-12} \\\Leftrightarrow &-6x & = &-5\\\Leftrightarrow & \color{red}{-6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-3}& = &-14 \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3} & = &-14\color{blue}{+3} \\\Leftrightarrow &-6x & = &-11\\\Leftrightarrow & \color{red}{-6}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-14}& = &-14 \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14} & = &-14\color{blue}{+14} \\\Leftrightarrow &12x & = &0\\\Leftrightarrow & \color{red}{12}x & = &0\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{0}{12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)