Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

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