Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+9}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+9}\color{blue}{-9-x } & = & 11 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 11 \color{blue}{-9} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+14}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14+11x } & = & 2 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &26x & = &-12\\\Leftrightarrow & \color{red}{26}x & = &-12\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-12}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+4}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-x } & = & 11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 11 \color{blue}{-4} \\\Leftrightarrow &-10x & = &7\\\Leftrightarrow & \color{red}{-10}x & = &7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+10}& = & 10 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{+10}\color{blue}{-10+5x } & = & 10 \color{red}{ -5x }\color{blue}{-10+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 10 \color{blue}{-10} \\\Leftrightarrow &13x & = &0\\\Leftrightarrow & \color{red}{13}x & = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-14}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14-9x } & = & 13 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 13 \color{blue}{+14} \\\Leftrightarrow &-13x & = &27\\\Leftrightarrow & \color{red}{-13}x & = &27\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{27}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{13} } & & \\ & V = \left\{ \frac{-27}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-1}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-1}\color{blue}{+1-x } & = & 3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-2}& = & -3 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{-2}\color{blue}{+2-12x } & = & -3 \color{red}{ +12x }\color{blue}{+2-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & -3 \color{blue}{+2} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+11}& = & 15 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11-14x } & = & 15 \color{red}{ +14x }\color{blue}{-11-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+3}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-13x } & = & -2 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -2 \color{blue}{-3} \\\Leftrightarrow &-25x & = &-5\\\Leftrightarrow & \color{red}{-25}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-5}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-4}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4-x } & = & -1 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -1 \color{blue}{+4} \\\Leftrightarrow &4x & = &3\\\Leftrightarrow & \color{red}{4}x & = &3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14-x } & = & -8 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -8 \color{blue}{-14} \\\Leftrightarrow &5x & = &-22\\\Leftrightarrow & \color{red}{5}x & = &-22\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-22}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{5} } & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{+2}& = & -1 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2+2x } & = & -1 \color{red}{ -2x }\color{blue}{-2+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -1 \color{blue}{-2} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)