Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+11}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11-4x } & = & -15 \color{red}{ +4x }\color{blue}{-11-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &-x & = &-26\\\Leftrightarrow & \color{red}{-}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-26}{-1} \\\Leftrightarrow & \color{green}{ x = 26 } & & \\ & V = \left\{ 26 \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{-13}& = & -10 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13-14x } & = & -10 \color{red}{ +14x }\color{blue}{+13-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & -10 \color{blue}{+13} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-1}& = & -12 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1-3x } & = & -12 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & -12 \color{blue}{+1} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+10}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-x } & = & -3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &-6x & = &-13\\\Leftrightarrow & \color{red}{-6}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-x } & = & -15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -15 \color{blue}{+1} \\\Leftrightarrow &-11x & = &-14\\\Leftrightarrow & \color{red}{-11}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{14}{11} } & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+4}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4-13x } & = & 13 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & 7x \color{blue}{-13x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &-6x & = &9\\\Leftrightarrow & \color{red}{-6}x & = &9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-1}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-x } & = & 4 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 4 \color{blue}{+1} \\\Leftrightarrow &-9x & = &5\\\Leftrightarrow & \color{red}{-9}x & = &5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-15}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15-x } & = & 13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{+15} \\\Leftrightarrow &-9x & = &28\\\Leftrightarrow & \color{red}{-9}x & = &28\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{28}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{9} } & & \\ & V = \left\{ \frac{-28}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15-x } & = & -8 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -8 \color{blue}{+15} \\\Leftrightarrow &12x & = &7\\\Leftrightarrow & \color{red}{12}x & = &7\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{7}{12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-9}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9-3x } & = & 10 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & -x \color{blue}{-3x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &-4x & = &19\\\Leftrightarrow & \color{red}{-4}x & = &19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{4} } & & \\ & V = \left\{ \frac{-19}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+14}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14-5x } & = & -4 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &x & = &-18\\\Leftrightarrow & \color{red}{}x & = &-18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -18 \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-2}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-2}\color{blue}{+2-7x } & = & 14 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 14 \color{blue}{+2} \\\Leftrightarrow &-5x & = &16\\\Leftrightarrow & \color{red}{-5}x & = &16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)