Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-11}& = & -12 \color{red}{ +6x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11-6x } & = & -12 \color{red}{ +6x }\color{blue}{+11-6x } \\\Leftrightarrow & 11x \color{blue}{-6x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &5x & = &-1\\\Leftrightarrow & \color{red}{5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-10}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10+11x } & = & -9 \color{red}{ -11x }\color{blue}{+10+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &15x & = &1\\\Leftrightarrow & \color{red}{15}x & = &1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-11}& = & 7 \color{red}{ -4x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11+4x } & = & 7 \color{red}{ -4x }\color{blue}{+11+4x } \\\Leftrightarrow & -x \color{blue}{+4x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &3x & = &18\\\Leftrightarrow & \color{red}{3}x & = &18\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{18}{3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+12}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12+11x } & = & 3 \color{red}{ -11x }\color{blue}{-12+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 3 \color{blue}{-12} \\\Leftrightarrow &17x & = &-9\\\Leftrightarrow & \color{red}{17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{17} } & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+6}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-7x } & = & -15 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -15 \color{blue}{-6} \\\Leftrightarrow &-16x & = &-21\\\Leftrightarrow & \color{red}{-16}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-21}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{21}{16} } & & \\ & V = \left\{ \frac{21}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-6}& = & -13 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6+4x } & = & -13 \color{red}{ -4x }\color{blue}{+6+4x } \\\Leftrightarrow & x \color{blue}{+4x } & = & -13 \color{blue}{+6} \\\Leftrightarrow &5x & = &-7\\\Leftrightarrow & \color{red}{5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-6}& = & 2 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6-6x } & = & 2 \color{red}{ +6x }\color{blue}{+6-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & 2 \color{blue}{+6} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-12}& = & 5 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12-5x } & = & 5 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & 9x \color{blue}{-5x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &4x & = &17\\\Leftrightarrow & \color{red}{4}x & = &17\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{17}{4} \\\Leftrightarrow & \color{green}{ x = \frac{17}{4} } & & \\ & V = \left\{ \frac{17}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-3}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3+11x } & = & -15 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & -15 \color{blue}{+3} \\\Leftrightarrow &20x & = &-12\\\Leftrightarrow & \color{red}{20}x & = &-12\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-12}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+6}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6-x } & = & -8 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -8 \color{blue}{-6} \\\Leftrightarrow &11x & = &-14\\\Leftrightarrow & \color{red}{11}x & = &-14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-5}& = & 9 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5-3x } & = & 9 \color{red}{ +3x }\color{blue}{+5-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & 9 \color{blue}{+5} \\\Leftrightarrow &-5x & = &14\\\Leftrightarrow & \color{red}{-5}x & = &14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{5} } & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+15}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-x } & = & -13 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &-10x & = &-28\\\Leftrightarrow & \color{red}{-10}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-28}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)