Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-8}& = &7 \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8} & = &7\color{blue}{+8} \\\Leftrightarrow &-4x & = &15\\\Leftrightarrow & \color{red}{-4}x & = &15\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{15}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{4} } & & \\ & V = \left\{ \frac{-15}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+12}& = &-1 \\\Leftrightarrow & 14x \color{red}{+12}\color{blue}{-12} & = &-1\color{blue}{-12} \\\Leftrightarrow &14x & = &-13\\\Leftrightarrow & \color{red}{14}x & = &-13\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-13}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{14} } & & \\ & V = \left\{ \frac{-13}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+1}& = &-12 \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1} & = &-12\color{blue}{-1} \\\Leftrightarrow &6x & = &-13\\\Leftrightarrow & \color{red}{6}x & = &-13\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-13}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-7}& = &-7 \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7} & = &-7\color{blue}{+7} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+1}& = &9 \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1} & = &9\color{blue}{-1} \\\Leftrightarrow &9x & = &8\\\Leftrightarrow & \color{red}{9}x & = &8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-15}& = &10 \\\Leftrightarrow & x \color{red}{-15}\color{blue}{+15} & = &10\color{blue}{+15} \\\Leftrightarrow &x & = &25\\\Leftrightarrow & \color{red}{}x & = &25\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 25 \\\Leftrightarrow & \color{green}{ x = 25 } & & \\ & V = \left\{ 25 \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+15}& = &-15 \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15} & = &-15\color{blue}{-15} \\\Leftrightarrow &-9x & = &-30\\\Leftrightarrow & \color{red}{-9}x & = &-30\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-30}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-3}& = &1 \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3} & = &1\color{blue}{+3} \\\Leftrightarrow &9x & = &4\\\Leftrightarrow & \color{red}{9}x & = &4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-7}& = &12 \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7} & = &12\color{blue}{+7} \\\Leftrightarrow &10x & = &19\\\Leftrightarrow & \color{red}{10}x & = &19\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{19}{10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+11}& = &-11 \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11} & = &-11\color{blue}{-11} \\\Leftrightarrow &-x & = &-22\\\Leftrightarrow & \color{red}{-}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-22}{-1} \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+6}& = &-4 \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6} & = &-4\color{blue}{-6} \\\Leftrightarrow &4x & = &-10\\\Leftrightarrow & \color{red}{4}x & = &-10\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-10}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-6}& = &10 \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6} & = &10\color{blue}{+6} \\\Leftrightarrow &7x & = &16\\\Leftrightarrow & \color{red}{7}x & = &16\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{16}{7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)