Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+15}& = & -7 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15+7x } & = & -7 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &19x & = &-22\\\Leftrightarrow & \color{red}{19}x & = &-22\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-22}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{19} } & & \\ & V = \left\{ \frac{-22}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-12}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12-13x } & = & 8 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & 8 \color{blue}{+12} \\\Leftrightarrow &-11x & = &20\\\Leftrightarrow & \color{red}{-11}x & = &20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+14}& = & -12 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14+2x } & = & -12 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &13x & = &-26\\\Leftrightarrow & \color{red}{13}x & = &-26\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-26}{13} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+10}& = & -1 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10+3x } & = & -1 \color{red}{ -3x }\color{blue}{-10+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &7x & = &-11\\\Leftrightarrow & \color{red}{7}x & = &-11\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-11}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-x } & = & -8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-20\\\Leftrightarrow & \color{red}{-3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-x } & = & -11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &-9x & = &-24\\\Leftrightarrow & \color{red}{-9}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-24}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+9}& = & 11 \color{red}{ +14x } \\\Leftrightarrow & -x \color{red}{+9}\color{blue}{-9-14x } & = & 11 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & -x \color{blue}{-14x } & = & 11 \color{blue}{-9} \\\Leftrightarrow &-15x & = &2\\\Leftrightarrow & \color{red}{-15}x & = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+5}& = & 7 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5-2x } & = & 7 \color{red}{ +2x }\color{blue}{-5-2x } \\\Leftrightarrow & 13x \color{blue}{-2x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+3}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3-5x } & = & 4 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+8}& = & 15 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8-14x } & = & 15 \color{red}{ +14x }\color{blue}{-8-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & 15 \color{blue}{-8} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-13}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-7x } & = & 15 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &-17x & = &28\\\Leftrightarrow & \color{red}{-17}x & = &28\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{28}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{17} } & & \\ & V = \left\{ \frac{-28}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+12}& = & -8 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12+13x } & = & -8 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &23x & = &-20\\\Leftrightarrow & \color{red}{23}x & = &-20\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-20}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{23} } & & \\ & V = \left\{ \frac{-20}{23} \right\} & \\\end{align}\)