Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-6}& = & 1 \color{red}{ +14x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6-14x } & = & 1 \color{red}{ +14x }\color{blue}{+6-14x } \\\Leftrightarrow & x \color{blue}{-14x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &-13x & = &7\\\Leftrightarrow & \color{red}{-13}x & = &7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+7}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+7}\color{blue}{-7-7x } & = & -4 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -4 \color{blue}{-7} \\\Leftrightarrow &-20x & = &-11\\\Leftrightarrow & \color{red}{-20}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-11}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{11}{20} } & & \\ & V = \left\{ \frac{11}{20} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+7}& = & -15 \color{red}{ +2x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7-2x } & = & -15 \color{red}{ +2x }\color{blue}{-7-2x } \\\Leftrightarrow & x \color{blue}{-2x } & = & -15 \color{blue}{-7} \\\Leftrightarrow &-x & = &-22\\\Leftrightarrow & \color{red}{-}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-22}{-1} \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+11}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-x } & = & 2 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+9}& = & -9 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9-10x } & = & -9 \color{red}{ +10x }\color{blue}{-9-10x } \\\Leftrightarrow & x \color{blue}{-10x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+13}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13-x } & = & 2 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 2 \color{blue}{-13} \\\Leftrightarrow &-10x & = &-11\\\Leftrightarrow & \color{red}{-10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+5}& = & -11 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5-8x } & = & -11 \color{red}{ +8x }\color{blue}{-5-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &-7x & = &-16\\\Leftrightarrow & \color{red}{-7}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+1}& = & 8 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1+5x } & = & 8 \color{red}{ -5x }\color{blue}{-1+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 8 \color{blue}{-1} \\\Leftrightarrow &11x & = &7\\\Leftrightarrow & \color{red}{11}x & = &7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-1}\color{blue}{+1-x } & = & 5 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 5 \color{blue}{+1} \\\Leftrightarrow &-10x & = &6\\\Leftrightarrow & \color{red}{-10}x & = &6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-7}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7-x } & = & -10 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -10 \color{blue}{+7} \\\Leftrightarrow &10x & = &-3\\\Leftrightarrow & \color{red}{10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+2}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2-13x } & = & -14 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & -14 \color{blue}{-2} \\\Leftrightarrow &-12x & = &-16\\\Leftrightarrow & \color{red}{-12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+11}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11-x } & = & -3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -3 \color{blue}{-11} \\\Leftrightarrow &-12x & = &-14\\\Leftrightarrow & \color{red}{-12}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)