Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+12}& = & -2 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12+4x } & = & -2 \color{red}{ -4x }\color{blue}{-12+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -2 \color{blue}{-12} \\\Leftrightarrow &13x & = &-14\\\Leftrightarrow & \color{red}{13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-5}& = & 2 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-5}\color{blue}{+5+13x } & = & 2 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &27x & = &7\\\Leftrightarrow & \color{red}{27}x & = &7\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{7}{27} \\\Leftrightarrow & \color{green}{ x = \frac{7}{27} } & & \\ & V = \left\{ \frac{7}{27} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-x } & = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &-12x & = &14\\\Leftrightarrow & \color{red}{-12}x & = &14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-12}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-13x } & = & 6 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 6 \color{blue}{+12} \\\Leftrightarrow &-28x & = &18\\\Leftrightarrow & \color{red}{-28}x & = &18\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{18}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-5}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5-7x } & = & 10 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 10 \color{blue}{+5} \\\Leftrightarrow &-20x & = &15\\\Leftrightarrow & \color{red}{-20}x & = &15\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{15}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+6}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-13x } & = & -5 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &-25x & = &-11\\\Leftrightarrow & \color{red}{-25}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-11}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{11}{25} } & & \\ & V = \left\{ \frac{11}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+4}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-x } & = & -10 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &-9x & = &-14\\\Leftrightarrow & \color{red}{-9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13-x } & = & -14 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -14 \color{blue}{-13} \\\Leftrightarrow &7x & = &-27\\\Leftrightarrow & \color{red}{7}x & = &-27\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-27}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{7} } & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+10}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-x } & = & 11 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 11 \color{blue}{-10} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+7}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-x } & = & -2 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -2 \color{blue}{-7} \\\Leftrightarrow &-6x & = &-9\\\Leftrightarrow & \color{red}{-6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-2}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2-7x } & = & -11 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -11 \color{blue}{+2} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+2}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-13x } & = & 11 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 11 \color{blue}{-2} \\\Leftrightarrow &-25x & = &9\\\Leftrightarrow & \color{red}{-25}x & = &9\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{9}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{25} } & & \\ & V = \left\{ \frac{-9}{25} \right\} & \\\end{align}\)