Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+14}& = &-2 \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14} & = &-2\color{blue}{-14} \\\Leftrightarrow &13x & = &-16\\\Leftrightarrow & \color{red}{13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-3}& = &13 \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3} & = &13\color{blue}{+3} \\\Leftrightarrow &8x & = &16\\\Leftrightarrow & \color{red}{8}x & = &16\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{16}{8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+6}& = &6 \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6} & = &6\color{blue}{-6} \\\Leftrightarrow &15x & = &0\\\Leftrightarrow & \color{red}{15}x & = &0\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{0}{15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-3}& = &5 \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3} & = &5\color{blue}{+3} \\\Leftrightarrow &6x & = &8\\\Leftrightarrow & \color{red}{6}x & = &8\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{8}{6} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+10}& = &5 \\\Leftrightarrow & 12x \color{red}{+10}\color{blue}{-10} & = &5\color{blue}{-10} \\\Leftrightarrow &12x & = &-5\\\Leftrightarrow & \color{red}{12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+9}& = &9 \\\Leftrightarrow & 8x \color{red}{+9}\color{blue}{-9} & = &9\color{blue}{-9} \\\Leftrightarrow &8x & = &0\\\Leftrightarrow & \color{red}{8}x & = &0\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{0}{8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+1}& = &-12 \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1} & = &-12\color{blue}{-1} \\\Leftrightarrow &7x & = &-13\\\Leftrightarrow & \color{red}{7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-8}& = &-5 \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8} & = &-5\color{blue}{+8} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-11}& = &15 \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11} & = &15\color{blue}{+11} \\\Leftrightarrow &7x & = &26\\\Leftrightarrow & \color{red}{7}x & = &26\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{26}{7} \\\Leftrightarrow & \color{green}{ x = \frac{26}{7} } & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-10}& = &-15 \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10} & = &-15\color{blue}{+10} \\\Leftrightarrow &7x & = &-5\\\Leftrightarrow & \color{red}{7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-5}& = &15 \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5} & = &15\color{blue}{+5} \\\Leftrightarrow &-2x & = &20\\\Leftrightarrow & \color{red}{-2}x & = &20\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{20}{-2} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-5}& = &7 \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5} & = &7\color{blue}{+5} \\\Leftrightarrow &-4x & = &12\\\Leftrightarrow & \color{red}{-4}x & = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)