Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+12}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+12}\color{blue}{-12+13x } & = & 14 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &27x & = &2\\\Leftrightarrow & \color{red}{27}x & = &2\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{2}{27} \\\Leftrightarrow & \color{green}{ x = \frac{2}{27} } & & \\ & V = \left\{ \frac{2}{27} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-8}& = & -10 \color{red}{ +14x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8-14x } & = & -10 \color{red}{ +14x }\color{blue}{+8-14x } \\\Leftrightarrow & x \color{blue}{-14x } & = & -10 \color{blue}{+8} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-7}& = & -6 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7-12x } & = & -6 \color{red}{ +12x }\color{blue}{+7-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -6 \color{blue}{+7} \\\Leftrightarrow &-23x & = &1\\\Leftrightarrow & \color{red}{-23}x & = &1\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{1}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-1}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1-x } & = & 13 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &-4x & = &14\\\Leftrightarrow & \color{red}{-4}x & = &14\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{14}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-14}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14-4x } & = & 7 \color{red}{ +4x }\color{blue}{+14-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &7x & = &21\\\Leftrightarrow & \color{red}{7}x & = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-3}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3-x } & = & -14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -14 \color{blue}{+3} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13-x } & = & 7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &-15x & = &20\\\Leftrightarrow & \color{red}{-15}x & = &20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-x } & = & -7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &-8x & = &0\\\Leftrightarrow & \color{red}{-8}x & = &0\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{0}{-8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-10}& = & 12 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10+2x } & = & 12 \color{red}{ -2x }\color{blue}{+10+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &13x & = &22\\\Leftrightarrow & \color{red}{13}x & = &22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-5}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5-5x } & = & 13 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-x & = &18\\\Leftrightarrow & \color{red}{-}x & = &18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{18}{-1} \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13-x } & = & 11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &5x & = &24\\\Leftrightarrow & \color{red}{5}x & = &24\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{24}{5} \\\Leftrightarrow & \color{green}{ x = \frac{24}{5} } & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-6}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-7x } & = & 11 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &-13x & = &17\\\Leftrightarrow & \color{red}{-13}x & = &17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)