Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{-12}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12-x } & = & -5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &-15x & = &7\\\Leftrightarrow & \color{red}{-15}x & = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-11}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-x } & = & -2 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -2 \color{blue}{+11} \\\Leftrightarrow &-10x & = &9\\\Leftrightarrow & \color{red}{-10}x & = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-7}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-x } & = & -6 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -6 \color{blue}{+7} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-1}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1-9x } & = & -14 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -14 \color{blue}{+1} \\\Leftrightarrow &5x & = &-13\\\Leftrightarrow & \color{red}{5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-3}& = & -1 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3-10x } & = & -1 \color{red}{ +10x }\color{blue}{+3-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -1 \color{blue}{+3} \\\Leftrightarrow &-x & = &2\\\Leftrightarrow & \color{red}{-}x & = &2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{2}{-1} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9-x } & = & 13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &-12x & = &22\\\Leftrightarrow & \color{red}{-12}x & = &22\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{22}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+6}& = & 9 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6+9x } & = & 9 \color{red}{ -9x }\color{blue}{-6+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &19x & = &3\\\Leftrightarrow & \color{red}{19}x & = &3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+4}& = & 13 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-10x } & = & 13 \color{red}{ +10x }\color{blue}{-4-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &-19x & = &9\\\Leftrightarrow & \color{red}{-19}x & = &9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-3}& = & 12 \color{red}{ -12x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3+12x } & = & 12 \color{red}{ -12x }\color{blue}{+3+12x } \\\Leftrightarrow & x \color{blue}{+12x } & = & 12 \color{blue}{+3} \\\Leftrightarrow &13x & = &15\\\Leftrightarrow & \color{red}{13}x & = &15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{-1}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-4x } & = & 13 \color{red}{ +4x }\color{blue}{+1-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &-19x & = &14\\\Leftrightarrow & \color{red}{-19}x & = &14\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{14}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{19} } & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-10}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & -4 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -4 \color{blue}{+10} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-8}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{-8}\color{blue}{+8-13x } & = & 15 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & -x \color{blue}{-13x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &-14x & = &23\\\Leftrightarrow & \color{red}{-14}x & = &23\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{23}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{14} } & & \\ & V = \left\{ \frac{-23}{14} \right\} & \\\end{align}\)