Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-8}& = & 13 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-3x } & = & 13 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 13 \color{blue}{+8} \\\Leftrightarrow &-x & = &21\\\Leftrightarrow & \color{red}{-}x & = &21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{21}{-1} \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-11}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11-13x } & = & -1 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &-x & = &10\\\Leftrightarrow & \color{red}{-}x & = &10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{10}{-1} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+13}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-13x } & = & -13 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -13 \color{blue}{-13} \\\Leftrightarrow &-25x & = &-26\\\Leftrightarrow & \color{red}{-25}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-26}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{26}{25} } & & \\ & V = \left\{ \frac{26}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+12}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12-x } & = & -6 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -6 \color{blue}{-12} \\\Leftrightarrow &10x & = &-18\\\Leftrightarrow & \color{red}{10}x & = &-18\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-18}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-9}& = & 7 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9-12x } & = & 7 \color{red}{ +12x }\color{blue}{+9-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &-x & = &16\\\Leftrightarrow & \color{red}{-}x & = &16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{16}{-1} \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & 10 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 10 \color{blue}{+6} \\\Leftrightarrow &-4x & = &16\\\Leftrightarrow & \color{red}{-4}x & = &16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{16}{-4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+3}& = & -4 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-14x } & = & -4 \color{red}{ +14x }\color{blue}{-3-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &-23x & = &-7\\\Leftrightarrow & \color{red}{-23}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-7}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{7}{23} } & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-12}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12-9x } & = & 1 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-10}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-x } & = & 8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 8 \color{blue}{+10} \\\Leftrightarrow &x & = &18\\\Leftrightarrow & \color{red}{}x & = &18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 18 \\\Leftrightarrow & \color{green}{ x = 18 } & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-15}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-14x } & = & -1 \color{red}{ +14x }\color{blue}{+15-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &-23x & = &14\\\Leftrightarrow & \color{red}{-23}x & = &14\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{14}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{23} } & & \\ & V = \left\{ \frac{-14}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+9}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-x } & = & 1 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 1 \color{blue}{-9} \\\Leftrightarrow &-14x & = &-8\\\Leftrightarrow & \color{red}{-14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+3}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-13x } & = & -1 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -1 \color{blue}{-3} \\\Leftrightarrow &-19x & = &-4\\\Leftrightarrow & \color{red}{-19}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{4}{19} } & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)