Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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