Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-11}& = & -3 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11+14x } & = & -3 \color{red}{ -14x }\color{blue}{+11+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -3 \color{blue}{+11} \\\Leftrightarrow &17x & = &8\\\Leftrightarrow & \color{red}{17}x & = &8\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{8}{17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+5}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-x } & = & 5 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6-x } & = & 13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &-9x & = &19\\\Leftrightarrow & \color{red}{-9}x & = &19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-9}& = & 13 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9+4x } & = & 13 \color{red}{ -4x }\color{blue}{+9+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &9x & = &22\\\Leftrightarrow & \color{red}{9}x & = &22\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{22}{9} \\\Leftrightarrow & \color{green}{ x = \frac{22}{9} } & & \\ & V = \left\{ \frac{22}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+15}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15-4x } & = & 11 \color{red}{ +4x }\color{blue}{-15-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & 11 \color{blue}{-15} \\\Leftrightarrow &x & = &-4\\\Leftrightarrow & \color{red}{}x & = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+8}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-7x } & = & 14 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+9}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9-13x } & = & 5 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 5 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-4\\\Leftrightarrow & \color{red}{-9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-14}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14-13x } & = & -13 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &-3x & = &1\\\Leftrightarrow & \color{red}{-3}x & = &1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-12}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12-7x } & = & 13 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &2x & = &25\\\Leftrightarrow & \color{red}{2}x & = &25\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{25}{2} \\\Leftrightarrow & \color{green}{ x = \frac{25}{2} } & & \\ & V = \left\{ \frac{25}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+13}& = & 13 \color{red}{ +14x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13-14x } & = & 13 \color{red}{ +14x }\color{blue}{-13-14x } \\\Leftrightarrow & 9x \color{blue}{-14x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-8}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-x } & = & 8 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &-10x & = &16\\\Leftrightarrow & \color{red}{-10}x & = &16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-1}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1-7x } & = & -15 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & -15 \color{blue}{+1} \\\Leftrightarrow &-10x & = &-14\\\Leftrightarrow & \color{red}{-10}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)