Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-13}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13-3x } & = & 11 \color{red}{ +3x }\color{blue}{+13-3x } \\\Leftrightarrow & 5x \color{blue}{-3x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &2x & = &24\\\Leftrightarrow & \color{red}{2}x & = &24\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{24}{2} \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+6}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6-13x } & = & -11 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -11 \color{blue}{-6} \\\Leftrightarrow &-4x & = &-17\\\Leftrightarrow & \color{red}{-4}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-17}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{17}{4} } & & \\ & V = \left\{ \frac{17}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+1}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1-x } & = & -14 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -14 \color{blue}{-1} \\\Leftrightarrow &13x & = &-15\\\Leftrightarrow & \color{red}{13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-8}& = & 14 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8-9x } & = & 14 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & 14 \color{blue}{+8} \\\Leftrightarrow &x & = &22\\\Leftrightarrow & \color{red}{}x & = &22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 22 \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{+9}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-7x } & = & -2 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &-17x & = &-11\\\Leftrightarrow & \color{red}{-17}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-11}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{11}{17} } & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+6}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6-11x } & = & 7 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &-21x & = &1\\\Leftrightarrow & \color{red}{-21}x & = &1\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{1}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{21} } & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-6}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-6}\color{blue}{+6-11x } & = & 13 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &4x & = &19\\\Leftrightarrow & \color{red}{4}x & = &19\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{19}{4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-12}& = & -5 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-6x } & = & -5 \color{red}{ +6x }\color{blue}{+12-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &-11x & = &7\\\Leftrightarrow & \color{red}{-11}x & = &7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-2}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2-3x } & = & 5 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & 5 \color{blue}{+2} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+5}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5-x } & = & -5 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -5 \color{blue}{-5} \\\Leftrightarrow &7x & = &-10\\\Leftrightarrow & \color{red}{7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-10}& = & -14 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10-6x } & = & -14 \color{red}{ +6x }\color{blue}{+10-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & -14 \color{blue}{+10} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-12}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12-11x } & = & -4 \color{red}{ +11x }\color{blue}{+12-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &4x & = &8\\\Leftrightarrow & \color{red}{4}x & = &8\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{8}{4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)