Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{-5}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & -8 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -8 \color{blue}{+5} \\\Leftrightarrow &-15x & = &-3\\\Leftrightarrow & \color{red}{-15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+11}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11-9x } & = & -9 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -9 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-20\\\Leftrightarrow & \color{red}{-13}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-12}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-13x } & = & 8 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & 8 \color{blue}{+12} \\\Leftrightarrow &-15x & = &20\\\Leftrightarrow & \color{red}{-15}x & = &20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-6}& = & 12 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6+14x } & = & 12 \color{red}{ -14x }\color{blue}{+6+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &19x & = &18\\\Leftrightarrow & \color{red}{19}x & = &18\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{18}{19} \\\Leftrightarrow & \color{green}{ x = \frac{18}{19} } & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+15}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15-x } & = & 14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-10}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-x } & = & -12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &-8x & = &-2\\\Leftrightarrow & \color{red}{-8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-10}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10-5x } & = & -5 \color{red}{ +5x }\color{blue}{+10-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -5 \color{blue}{+10} \\\Leftrightarrow &7x & = &5\\\Leftrightarrow & \color{red}{7}x & = &5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+15}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+15}\color{blue}{-15-7x } & = & -4 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -4 \color{blue}{-15} \\\Leftrightarrow &-4x & = &-19\\\Leftrightarrow & \color{red}{-4}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-14}& = & -1 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14+13x } & = & -1 \color{red}{ -13x }\color{blue}{+14+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &12x & = &13\\\Leftrightarrow & \color{red}{12}x & = &13\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{13}{12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-7}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7-3x } & = & 14 \color{red}{ +3x }\color{blue}{+7-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &7x & = &21\\\Leftrightarrow & \color{red}{7}x & = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-5}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5+11x } & = & 6 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 6 \color{blue}{+5} \\\Leftrightarrow &17x & = &11\\\Leftrightarrow & \color{red}{17}x & = &11\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{11}{17} \\\Leftrightarrow & \color{green}{ x = \frac{11}{17} } & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-15}& = & -7 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15+8x } & = & -7 \color{red}{ -8x }\color{blue}{+15+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &19x & = &8\\\Leftrightarrow & \color{red}{19}x & = &8\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{8}{19} \\\Leftrightarrow & \color{green}{ x = \frac{8}{19} } & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)