Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+9}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & -4 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -4 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-13\\\Leftrightarrow & \color{red}{-9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+5}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-13x } & = & 9 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 9 \color{blue}{-5} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+14}& = & 6 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-14x } & = & 6 \color{red}{ +14x }\color{blue}{-14-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 6 \color{blue}{-14} \\\Leftrightarrow &-27x & = &-8\\\Leftrightarrow & \color{red}{-27}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-8}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{8}{27} } & & \\ & V = \left\{ \frac{8}{27} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+3}& = & -6 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3-12x } & = & -6 \color{red}{ +12x }\color{blue}{-3-12x } \\\Leftrightarrow & 13x \color{blue}{-12x } & = & -6 \color{blue}{-3} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-4}& = & -14 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4+15x } & = & -14 \color{red}{ -15x }\color{blue}{+4+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &28x & = &-10\\\Leftrightarrow & \color{red}{28}x & = &-10\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{-10}{28} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+10}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10+11x } & = & -15 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -15 \color{blue}{-10} \\\Leftrightarrow &14x & = &-25\\\Leftrightarrow & \color{red}{14}x & = &-25\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-25}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{14} } & & \\ & V = \left\{ \frac{-25}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-6}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-x } & = & 15 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &-7x & = &21\\\Leftrightarrow & \color{red}{-7}x & = &21\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{21}{-7} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+14}& = & -2 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14-9x } & = & -2 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &5x & = &-16\\\Leftrightarrow & \color{red}{5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+11}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11-5x } & = & 7 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &-17x & = &-4\\\Leftrightarrow & \color{red}{-17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6-x } & = & 10 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 10 \color{blue}{-6} \\\Leftrightarrow &-11x & = &4\\\Leftrightarrow & \color{red}{-11}x & = &4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-12}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12-x } & = & -5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &-15x & = &7\\\Leftrightarrow & \color{red}{-15}x & = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+6}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6-13x } & = & 7 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)