Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+9}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9-7x } & = & -6 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &5x & = &-15\\\Leftrightarrow & \color{red}{5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-7}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-7x } & = & -3 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+5}& = & 3 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5+8x } & = & 3 \color{red}{ -8x }\color{blue}{-5+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &17x & = &-2\\\Leftrightarrow & \color{red}{17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+12}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-13x } & = & 9 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &-17x & = &-3\\\Leftrightarrow & \color{red}{-17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-11}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11-5x } & = & 15 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &7x & = &26\\\Leftrightarrow & \color{red}{7}x & = &26\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{26}{7} \\\Leftrightarrow & \color{green}{ x = \frac{26}{7} } & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+10}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10-3x } & = & 5 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & 5x \color{blue}{-3x } & = & 5 \color{blue}{-10} \\\Leftrightarrow &2x & = &-5\\\Leftrightarrow & \color{red}{2}x & = &-5\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-5}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+7}& = & -12 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7+11x } & = & -12 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &17x & = &-19\\\Leftrightarrow & \color{red}{17}x & = &-19\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-19}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{17} } & & \\ & V = \left\{ \frac{-19}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+7}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-x } & = & -8 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -8 \color{blue}{-7} \\\Leftrightarrow &-15x & = &-15\\\Leftrightarrow & \color{red}{-15}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-15}{-15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+8}& = & -4 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8+3x } & = & -4 \color{red}{ -3x }\color{blue}{-8+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -4 \color{blue}{-8} \\\Leftrightarrow &10x & = &-12\\\Leftrightarrow & \color{red}{10}x & = &-12\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-12}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-10}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10+13x } & = & -10 \color{red}{ -13x }\color{blue}{+10+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -10 \color{blue}{+10} \\\Leftrightarrow &23x & = &0\\\Leftrightarrow & \color{red}{23}x & = &0\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{0}{23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-4}\color{blue}{+4-x } & = & -3 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13-x } & = & -11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)