Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+3}& = &-8 \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3} & = &-8\color{blue}{-3} \\\Leftrightarrow &9x & = &-11\\\Leftrightarrow & \color{red}{9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+14}& = &14 \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14} & = &14\color{blue}{-14} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-10}& = &9 \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10} & = &9\color{blue}{+10} \\\Leftrightarrow &5x & = &19\\\Leftrightarrow & \color{red}{5}x & = &19\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{19}{5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-14}& = &-8 \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14} & = &-8\color{blue}{+14} \\\Leftrightarrow &-3x & = &6\\\Leftrightarrow & \color{red}{-3}x & = &6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{6}{-3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+5}& = &-14 \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5} & = &-14\color{blue}{-5} \\\Leftrightarrow &10x & = &-19\\\Leftrightarrow & \color{red}{10}x & = &-19\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-19}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{10} } & & \\ & V = \left\{ \frac{-19}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+9}& = &15 \\\Leftrightarrow & -x \color{red}{+9}\color{blue}{-9} & = &15\color{blue}{-9} \\\Leftrightarrow &-x & = &6\\\Leftrightarrow & \color{red}{-}x & = &6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{6}{-1} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+7}& = &3 \\\Leftrightarrow & 7x \color{red}{+7}\color{blue}{-7} & = &3\color{blue}{-7} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+3}& = &10 \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3} & = &10\color{blue}{-3} \\\Leftrightarrow &7x & = &7\\\Leftrightarrow & \color{red}{7}x & = &7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{7}{7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+4}& = &-14 \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4} & = &-14\color{blue}{-4} \\\Leftrightarrow &x & = &-18\\\Leftrightarrow & \color{red}{}x & = &-18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -18 \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+5}& = &-13 \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5} & = &-13\color{blue}{-5} \\\Leftrightarrow &3x & = &-18\\\Leftrightarrow & \color{red}{3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-18}{3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+9}& = &13 \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9} & = &13\color{blue}{-9} \\\Leftrightarrow &-8x & = &4\\\Leftrightarrow & \color{red}{-8}x & = &4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+1}& = &-11 \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1} & = &-11\color{blue}{-1} \\\Leftrightarrow &9x & = &-12\\\Leftrightarrow & \color{red}{9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)