Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-10}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & -2 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -2 \color{blue}{+10} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-1}& = & -2 \color{red}{ +14x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1-14x } & = & -2 \color{red}{ +14x }\color{blue}{+1-14x } \\\Leftrightarrow & 9x \color{blue}{-14x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-14}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14-11x } & = & 10 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & 13x \color{blue}{-11x } & = & 10 \color{blue}{+14} \\\Leftrightarrow &2x & = &24\\\Leftrightarrow & \color{red}{2}x & = &24\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{24}{2} \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+14}& = & -11 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14+4x } & = & -11 \color{red}{ -4x }\color{blue}{-14+4x } \\\Leftrightarrow & 13x \color{blue}{+4x } & = & -11 \color{blue}{-14} \\\Leftrightarrow &17x & = &-25\\\Leftrightarrow & \color{red}{17}x & = &-25\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-25}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{17} } & & \\ & V = \left\{ \frac{-25}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-1}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1-5x } & = & 8 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8-x } & = & 10 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &-12x & = &18\\\Leftrightarrow & \color{red}{-12}x & = &18\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{18}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-4}& = & -4 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4-6x } & = & -4 \color{red}{ +6x }\color{blue}{+4-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & -4 \color{blue}{+4} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+1}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1+13x } & = & 3 \color{red}{ -13x }\color{blue}{-1+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &20x & = &2\\\Leftrightarrow & \color{red}{20}x & = &2\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{2}{20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+3}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3-4x } & = & 13 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & x \color{blue}{-4x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &-3x & = &10\\\Leftrightarrow & \color{red}{-3}x & = &10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+10}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10-11x } & = & 1 \color{red}{ +11x }\color{blue}{-10-11x } \\\Leftrightarrow & 3x \color{blue}{-11x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &-8x & = &-9\\\Leftrightarrow & \color{red}{-8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+1}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1-13x } & = & 12 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &-12x & = &11\\\Leftrightarrow & \color{red}{-12}x & = &11\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{11}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+5}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-7x } & = & 11 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)