Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-9}& = &1 \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9} & = &1\color{blue}{+9} \\\Leftrightarrow &10x & = &10\\\Leftrightarrow & \color{red}{10}x & = &10\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{10}{10} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-7}& = &-13 \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7} & = &-13\color{blue}{+7} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-13}& = &8 \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13} & = &8\color{blue}{+13} \\\Leftrightarrow &8x & = &21\\\Leftrightarrow & \color{red}{8}x & = &21\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{21}{8} \\\Leftrightarrow & \color{green}{ x = \frac{21}{8} } & & \\ & V = \left\{ \frac{21}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+10}& = &-3 \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10} & = &-3\color{blue}{-10} \\\Leftrightarrow &-3x & = &-13\\\Leftrightarrow & \color{red}{-3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{+1}& = &-8 \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1} & = &-8\color{blue}{-1} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-12}& = &12 \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12} & = &12\color{blue}{+12} \\\Leftrightarrow &11x & = &24\\\Leftrightarrow & \color{red}{11}x & = &24\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{24}{11} \\\Leftrightarrow & \color{green}{ x = \frac{24}{11} } & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-12}& = &1 \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12} & = &1\color{blue}{+12} \\\Leftrightarrow &3x & = &13\\\Leftrightarrow & \color{red}{3}x & = &13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+13}& = &9 \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13} & = &9\color{blue}{-13} \\\Leftrightarrow &-10x & = &-4\\\Leftrightarrow & \color{red}{-10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+10}& = &-10 \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10} & = &-10\color{blue}{-10} \\\Leftrightarrow &9x & = &-20\\\Leftrightarrow & \color{red}{9}x & = &-20\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-20}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{9} } & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+5}& = &9 \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5} & = &9\color{blue}{-5} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+2}& = &10 \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2} & = &10\color{blue}{-2} \\\Leftrightarrow &-2x & = &8\\\Leftrightarrow & \color{red}{-2}x & = &8\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{8}{-2} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-9}& = &-12 \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9} & = &-12\color{blue}{+9} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)