Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+9}& = & -12 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{+9}\color{blue}{-9-4x } & = & -12 \color{red}{ +4x }\color{blue}{-9-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & -12 \color{blue}{-9} \\\Leftrightarrow &x & = &-21\\\Leftrightarrow & \color{red}{}x & = &-21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -21 \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+7}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-x } & = & -13 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &x & = &-20\\\Leftrightarrow & \color{red}{}x & = &-20\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -20 \\\Leftrightarrow & \color{green}{ x = -20 } & & \\ & V = \left\{ -20 \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+10}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-x } & = & 8 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 8 \color{blue}{-10} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-11}& = & 8 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11+9x } & = & 8 \color{red}{ -9x }\color{blue}{+11+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 8 \color{blue}{+11} \\\Leftrightarrow &14x & = &19\\\Leftrightarrow & \color{red}{14}x & = &19\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{19}{14} \\\Leftrightarrow & \color{green}{ x = \frac{19}{14} } & & \\ & V = \left\{ \frac{19}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+12}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-x } & = & 6 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 6 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+14}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & -14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -14 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-28\\\Leftrightarrow & \color{red}{-9}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-28}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{28}{9} } & & \\ & V = \left\{ \frac{28}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-3}& = & 9 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3-9x } & = & 9 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 9 \color{blue}{+3} \\\Leftrightarrow &5x & = &12\\\Leftrightarrow & \color{red}{5}x & = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+8}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8-x } & = & 15 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 15 \color{blue}{-8} \\\Leftrightarrow &-13x & = &7\\\Leftrightarrow & \color{red}{-13}x & = &7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1-x } & = & -10 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -10 \color{blue}{+1} \\\Leftrightarrow &-5x & = &-9\\\Leftrightarrow & \color{red}{-5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-3}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{-3}\color{blue}{+3-3x } & = & -11 \color{red}{ +3x }\color{blue}{+3-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &-5x & = &-8\\\Leftrightarrow & \color{red}{-5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+12}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-x } & = & 3 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 3 \color{blue}{-12} \\\Leftrightarrow &-12x & = &-9\\\Leftrightarrow & \color{red}{-12}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+15}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-x } & = & 15 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 15 \color{blue}{-15} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)