Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-12}& = & -13 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+2x } & = & -13 \color{red}{ -2x }\color{blue}{+12+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -13 \color{blue}{+12} \\\Leftrightarrow &5x & = &-1\\\Leftrightarrow & \color{red}{5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+14}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14-8x } & = & 13 \color{red}{ +8x }\color{blue}{-14-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+6}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6-7x } & = & -13 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & x \color{blue}{-7x } & = & -13 \color{blue}{-6} \\\Leftrightarrow &-6x & = &-19\\\Leftrightarrow & \color{red}{-6}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{19}{6} } & & \\ & V = \left\{ \frac{19}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+13}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13-x } & = & -8 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -8 \color{blue}{-13} \\\Leftrightarrow &13x & = &-21\\\Leftrightarrow & \color{red}{13}x & = &-21\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-21}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{13} } & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+3}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-x } & = & 2 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &-14x & = &-1\\\Leftrightarrow & \color{red}{-14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+10}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10-11x } & = & -11 \color{red}{ +11x }\color{blue}{-10-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &-2x & = &-21\\\Leftrightarrow & \color{red}{-2}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-21}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{21}{2} } & & \\ & V = \left\{ \frac{21}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-5}& = & 9 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5-9x } & = & 9 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 9 \color{blue}{+5} \\\Leftrightarrow &-x & = &14\\\Leftrightarrow & \color{red}{-}x & = &14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{14}{-1} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-6}& = & -6 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-12x } & = & -6 \color{red}{ +12x }\color{blue}{+6-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &-23x & = &0\\\Leftrightarrow & \color{red}{-23}x & = &0\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{0}{-23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+11}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11-3x } & = & 11 \color{red}{ +3x }\color{blue}{-11-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & 11 \color{blue}{-11} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+5}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-x } & = & -15 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &-3x & = &-20\\\Leftrightarrow & \color{red}{-3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+10}& = & 5 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10+2x } & = & 5 \color{red}{ -2x }\color{blue}{-10+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & 5 \color{blue}{-10} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-4}& = & 4 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4+13x } & = & 4 \color{red}{ -13x }\color{blue}{+4+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &20x & = &8\\\Leftrightarrow & \color{red}{20}x & = &8\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{8}{20} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)