Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+12}& = &-2 \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12} & = &-2\color{blue}{-12} \\\Leftrightarrow &3x & = &-14\\\Leftrightarrow & \color{red}{3}x & = &-14\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-14}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+2}& = &-4 \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2} & = &-4\color{blue}{-2} \\\Leftrightarrow &7x & = &-6\\\Leftrightarrow & \color{red}{7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+6}& = &-15 \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6} & = &-15\color{blue}{-6} \\\Leftrightarrow &3x & = &-21\\\Leftrightarrow & \color{red}{3}x & = &-21\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-21}{3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-3}& = &14 \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3} & = &14\color{blue}{+3} \\\Leftrightarrow &13x & = &17\\\Leftrightarrow & \color{red}{13}x & = &17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-4}& = &-7 \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4} & = &-7\color{blue}{+4} \\\Leftrightarrow &8x & = &-3\\\Leftrightarrow & \color{red}{8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+5}& = &-13 \\\Leftrightarrow & 2x \color{red}{+5}\color{blue}{-5} & = &-13\color{blue}{-5} \\\Leftrightarrow &2x & = &-18\\\Leftrightarrow & \color{red}{2}x & = &-18\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-18}{2} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-12}& = &-3 \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12} & = &-3\color{blue}{+12} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-8}& = &-13 \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8} & = &-13\color{blue}{+8} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+12}& = &-13 \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12} & = &-13\color{blue}{-12} \\\Leftrightarrow &8x & = &-25\\\Leftrightarrow & \color{red}{8}x & = &-25\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-25}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{8} } & & \\ & V = \left\{ \frac{-25}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-13}& = &-9 \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13} & = &-9\color{blue}{+13} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+5}& = &-3 \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5} & = &-3\color{blue}{-5} \\\Leftrightarrow &-10x & = &-8\\\Leftrightarrow & \color{red}{-10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+12}& = &-1 \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12} & = &-1\color{blue}{-12} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)