Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+2}& = &-1 \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2} & = &-1\color{blue}{-2} \\\Leftrightarrow &10x & = &-3\\\Leftrightarrow & \color{red}{10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-5}& = &-10 \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5} & = &-10\color{blue}{+5} \\\Leftrightarrow &-2x & = &-5\\\Leftrightarrow & \color{red}{-2}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-5}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+3}& = &1 \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3} & = &1\color{blue}{-3} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-1}& = &-5 \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1} & = &-5\color{blue}{+1} \\\Leftrightarrow &15x & = &-4\\\Leftrightarrow & \color{red}{15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+13}& = &-5 \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13} & = &-5\color{blue}{-13} \\\Leftrightarrow &5x & = &-18\\\Leftrightarrow & \color{red}{5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+15}& = &-5 \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15} & = &-5\color{blue}{-15} \\\Leftrightarrow &-8x & = &-20\\\Leftrightarrow & \color{red}{-8}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-10}& = &-10 \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10} & = &-10\color{blue}{+10} \\\Leftrightarrow &9x & = &0\\\Leftrightarrow & \color{red}{9}x & = &0\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{0}{9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-8}& = &5 \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8} & = &5\color{blue}{+8} \\\Leftrightarrow &-14x & = &13\\\Leftrightarrow & \color{red}{-14}x & = &13\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{13}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{14} } & & \\ & V = \left\{ \frac{-13}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+10}& = &15 \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10} & = &15\color{blue}{-10} \\\Leftrightarrow &6x & = &5\\\Leftrightarrow & \color{red}{6}x & = &5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+1}& = &-4 \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1} & = &-4\color{blue}{-1} \\\Leftrightarrow &-8x & = &-5\\\Leftrightarrow & \color{red}{-8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+13}& = &-12 \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13} & = &-12\color{blue}{-13} \\\Leftrightarrow &9x & = &-25\\\Leftrightarrow & \color{red}{9}x & = &-25\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-25}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{9} } & & \\ & V = \left\{ \frac{-25}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-8}& = &15 \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8} & = &15\color{blue}{+8} \\\Leftrightarrow &-2x & = &23\\\Leftrightarrow & \color{red}{-2}x & = &23\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{23}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{2} } & & \\ & V = \left\{ \frac{-23}{2} \right\} & \\\end{align}\)