Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

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