Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+15}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15-9x } & = & -1 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-16\\\Leftrightarrow & \color{red}{-5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13-x } & = & 7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &-13x & = &20\\\Leftrightarrow & \color{red}{-13}x & = &20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{13} } & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-8}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8-x } & = & 15 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &-12x & = &23\\\Leftrightarrow & \color{red}{-12}x & = &23\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{23}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{12} } & & \\ & V = \left\{ \frac{-23}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-x } & = & -3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-12}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12-9x } & = & -8 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &-5x & = &4\\\Leftrightarrow & \color{red}{-5}x & = &4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+9}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & -12 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -12 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-21\\\Leftrightarrow & \color{red}{-9}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-15}& = & 15 \color{red}{ -3x } \\\Leftrightarrow & x \color{red}{-15}\color{blue}{+15+3x } & = & 15 \color{red}{ -3x }\color{blue}{+15+3x } \\\Leftrightarrow & x \color{blue}{+3x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &4x & = &30\\\Leftrightarrow & \color{red}{4}x & = &30\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{30}{4} \\\Leftrightarrow & \color{green}{ x = \frac{15}{2} } & & \\ & V = \left\{ \frac{15}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-3}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-x } & = & 8 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 8 \color{blue}{+3} \\\Leftrightarrow &-8x & = &11\\\Leftrightarrow & \color{red}{-8}x & = &11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-3}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-x } & = & 2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &-4x & = &5\\\Leftrightarrow & \color{red}{-4}x & = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+14}& = & -10 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14-12x } & = & -10 \color{red}{ +12x }\color{blue}{-14-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -10 \color{blue}{-14} \\\Leftrightarrow &-x & = &-24\\\Leftrightarrow & \color{red}{-}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-24}{-1} \\\Leftrightarrow & \color{green}{ x = 24 } & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+11}& = & -8 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11+2x } & = & -8 \color{red}{ -2x }\color{blue}{-11+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &5x & = &-19\\\Leftrightarrow & \color{red}{5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-19}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-13}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-x } & = & -12 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)