Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-11}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-x } & = & 8 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 8 \color{blue}{+11} \\\Leftrightarrow &-9x & = &19\\\Leftrightarrow & \color{red}{-9}x & = &19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+14}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-13x } & = & 2 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &-25x & = &-12\\\Leftrightarrow & \color{red}{-25}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-12}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{12}{25} } & & \\ & V = \left\{ \frac{12}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-6}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6-3x } & = & 14 \color{red}{ +3x }\color{blue}{+6-3x } \\\Leftrightarrow & x \color{blue}{-3x } & = & 14 \color{blue}{+6} \\\Leftrightarrow &-2x & = &20\\\Leftrightarrow & \color{red}{-2}x & = &20\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{20}{-2} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-11}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11-x } & = & 8 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 8 \color{blue}{+11} \\\Leftrightarrow &13x & = &19\\\Leftrightarrow & \color{red}{13}x & = &19\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{19}{13} \\\Leftrightarrow & \color{green}{ x = \frac{19}{13} } & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+12}& = & 4 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12+9x } & = & 4 \color{red}{ -9x }\color{blue}{-12+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 4 \color{blue}{-12} \\\Leftrightarrow &14x & = &-8\\\Leftrightarrow & \color{red}{14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-8}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-1}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1-3x } & = & -11 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & -11 \color{blue}{+1} \\\Leftrightarrow &5x & = &-10\\\Leftrightarrow & \color{red}{5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-10}{5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-6}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-6}\color{blue}{+6-x } & = & -4 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6-x } & = & -7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &-11x & = &-13\\\Leftrightarrow & \color{red}{-11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+11}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11-x } & = & 4 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 4 \color{blue}{-11} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-4}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & 11x \color{red}{-4}\color{blue}{+4-9x } & = & 15 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & 11x \color{blue}{-9x } & = & 15 \color{blue}{+4} \\\Leftrightarrow &2x & = &19\\\Leftrightarrow & \color{red}{2}x & = &19\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{19}{2} \\\Leftrightarrow & \color{green}{ x = \frac{19}{2} } & & \\ & V = \left\{ \frac{19}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+9}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9+11x } & = & -3 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -3 \color{blue}{-9} \\\Leftrightarrow &15x & = &-12\\\Leftrightarrow & \color{red}{15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-12}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{+3}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3-13x } & = & 4 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)