Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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