Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-x } & = & 4 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 4 \color{blue}{+13} \\\Leftrightarrow &-12x & = &17\\\Leftrightarrow & \color{red}{-12}x & = &17\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{17}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{12} } & & \\ & V = \left\{ \frac{-17}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+5}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5-7x } & = & -10 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -10 \color{blue}{-5} \\\Leftrightarrow &5x & = &-15\\\Leftrightarrow & \color{red}{5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-13}& = & 10 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13+9x } & = & 10 \color{red}{ -9x }\color{blue}{+13+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &14x & = &23\\\Leftrightarrow & \color{red}{14}x & = &23\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{23}{14} \\\Leftrightarrow & \color{green}{ x = \frac{23}{14} } & & \\ & V = \left\{ \frac{23}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+2}& = & 5 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-5x } & = & 5 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 5 \color{blue}{-2} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+9}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-7x } & = & 11 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 11 \color{blue}{-9} \\\Leftrightarrow &-20x & = &2\\\Leftrightarrow & \color{red}{-20}x & = &2\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{2}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-14}& = & 15 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-8x } & = & 15 \color{red}{ +8x }\color{blue}{+14-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & 15 \color{blue}{+14} \\\Leftrightarrow &-21x & = &29\\\Leftrightarrow & \color{red}{-21}x & = &29\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{29}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{21} } & & \\ & V = \left\{ \frac{-29}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+7}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-x } & = & -12 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &-15x & = &-19\\\Leftrightarrow & \color{red}{-15}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{19}{15} } & & \\ & V = \left\{ \frac{19}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-5}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-5x } & = & 4 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &-14x & = &9\\\Leftrightarrow & \color{red}{-14}x & = &9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-6}& = & -11 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6-9x } & = & -11 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -11 \color{blue}{+6} \\\Leftrightarrow &-17x & = &-5\\\Leftrightarrow & \color{red}{-17}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-5}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{5}{17} } & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+3}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3-3x } & = & -11 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & -11 \color{blue}{-3} \\\Leftrightarrow &11x & = &-14\\\Leftrightarrow & \color{red}{11}x & = &-14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-x } & = & 9 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 9 \color{blue}{+6} \\\Leftrightarrow &-12x & = &15\\\Leftrightarrow & \color{red}{-12}x & = &15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+3}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-x } & = & -5 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -5 \color{blue}{-3} \\\Leftrightarrow &-6x & = &-8\\\Leftrightarrow & \color{red}{-6}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)