Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+12}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12-x } & = & 2 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &10x & = &-10\\\Leftrightarrow & \color{red}{10}x & = &-10\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-10}{10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-x } & = & -10 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &-10x & = &-12\\\Leftrightarrow & \color{red}{-10}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-12}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+9}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9+3x } & = & 13 \color{red}{ -3x }\color{blue}{-9+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 13 \color{blue}{-9} \\\Leftrightarrow &7x & = &4\\\Leftrightarrow & \color{red}{7}x & = &4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-8}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-x } & = & -4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+2}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-x } & = & 13 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &-7x & = &11\\\Leftrightarrow & \color{red}{-7}x & = &11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+10}& = & -1 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10+13x } & = & -1 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &20x & = &-11\\\Leftrightarrow & \color{red}{20}x & = &-11\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-11}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{20} } & & \\ & V = \left\{ \frac{-11}{20} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+10}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10+11x } & = & 4 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 4 \color{blue}{-10} \\\Leftrightarrow &17x & = &-6\\\Leftrightarrow & \color{red}{17}x & = &-6\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-6}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+8}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-x } & = & 5 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+7}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-5x } & = & -12 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &-9x & = &-19\\\Leftrightarrow & \color{red}{-9}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{19}{9} } & & \\ & V = \left\{ \frac{19}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-5}& = & 11 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5+13x } & = & 11 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &20x & = &16\\\Leftrightarrow & \color{red}{20}x & = &16\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{16}{20} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2-x } & = & -11 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -11 \color{blue}{+2} \\\Leftrightarrow &-4x & = &-9\\\Leftrightarrow & \color{red}{-4}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-15}& = & 11 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-9x } & = & 11 \color{red}{ +9x }\color{blue}{+15-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &-x & = &26\\\Leftrightarrow & \color{red}{-}x & = &26\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{26}{-1} \\\Leftrightarrow & \color{green}{ x = -26 } & & \\ & V = \left\{ -26 \right\} & \\\end{align}\)