Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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