Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-10}& = &-1 \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10} & = &-1\color{blue}{+10} \\\Leftrightarrow &14x & = &9\\\Leftrightarrow & \color{red}{14}x & = &9\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{9}{14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-12}& = &-4 \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12} & = &-4\color{blue}{+12} \\\Leftrightarrow &11x & = &8\\\Leftrightarrow & \color{red}{11}x & = &8\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{8}{11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-9}& = &-9 \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9} & = &-9\color{blue}{+9} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+3}& = &-13 \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3} & = &-13\color{blue}{-3} \\\Leftrightarrow &-4x & = &-16\\\Leftrightarrow & \color{red}{-4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-16}{-4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-14}& = &-14 \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14} & = &-14\color{blue}{+14} \\\Leftrightarrow &-12x & = &0\\\Leftrightarrow & \color{red}{-12}x & = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-11}& = &5 \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11} & = &5\color{blue}{+11} \\\Leftrightarrow &2x & = &16\\\Leftrightarrow & \color{red}{2}x & = &16\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{16}{2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-10}& = &13 \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10} & = &13\color{blue}{+10} \\\Leftrightarrow &-9x & = &23\\\Leftrightarrow & \color{red}{-9}x & = &23\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{23}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{9} } & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+6}& = &14 \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6} & = &14\color{blue}{-6} \\\Leftrightarrow &3x & = &8\\\Leftrightarrow & \color{red}{3}x & = &8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+15}& = &-7 \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15} & = &-7\color{blue}{-15} \\\Leftrightarrow &2x & = &-22\\\Leftrightarrow & \color{red}{2}x & = &-22\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-22}{2} \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-5}& = &-12 \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5} & = &-12\color{blue}{+5} \\\Leftrightarrow &4x & = &-7\\\Leftrightarrow & \color{red}{4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-7}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-9}& = &-12 \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9} & = &-12\color{blue}{+9} \\\Leftrightarrow &-6x & = &-3\\\Leftrightarrow & \color{red}{-6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+12}& = &7 \\\Leftrightarrow & x \color{red}{+12}\color{blue}{-12} & = &7\color{blue}{-12} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)