Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+5}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5-4x } & = & -5 \color{red}{ +4x }\color{blue}{-5-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & -5 \color{blue}{-5} \\\Leftrightarrow &-x & = &-10\\\Leftrightarrow & \color{red}{-}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-10}{-1} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+3}& = & 2 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3+4x } & = & 2 \color{red}{ -4x }\color{blue}{-3+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &9x & = &-1\\\Leftrightarrow & \color{red}{9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+8}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8-3x } & = & -3 \color{red}{ +3x }\color{blue}{-8-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &-14x & = &-11\\\Leftrightarrow & \color{red}{-14}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{11}{14} } & & \\ & V = \left\{ \frac{11}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+4}& = & -1 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-3x } & = & -1 \color{red}{ +3x }\color{blue}{-4-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -1 \color{blue}{-4} \\\Leftrightarrow &-x & = &-5\\\Leftrightarrow & \color{red}{-}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-5}{-1} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-6}& = & 8 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6+4x } & = & 8 \color{red}{ -4x }\color{blue}{+6+4x } \\\Leftrightarrow & 13x \color{blue}{+4x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &17x & = &14\\\Leftrightarrow & \color{red}{17}x & = &14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+10}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-x } & = & -12 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -12 \color{blue}{-10} \\\Leftrightarrow &-12x & = &-22\\\Leftrightarrow & \color{red}{-12}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-22}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-3}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-7x } & = & -11 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &-20x & = &-8\\\Leftrightarrow & \color{red}{-20}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-8}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+12}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12-11x } & = & -14 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -14 \color{blue}{-12} \\\Leftrightarrow &-6x & = &-26\\\Leftrightarrow & \color{red}{-6}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-26}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+3}& = & -3 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3+5x } & = & -3 \color{red}{ -5x }\color{blue}{-3+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -3 \color{blue}{-3} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+11}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11-x } & = & 15 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &4x & = &4\\\Leftrightarrow & \color{red}{4}x & = &4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{4}{4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+1}& = & -12 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1+11x } & = & -12 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &23x & = &-13\\\Leftrightarrow & \color{red}{23}x & = &-13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{23} } & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-14}& = & -7 \color{red}{ +8x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14-8x } & = & -7 \color{red}{ +8x }\color{blue}{+14-8x } \\\Leftrightarrow & 9x \color{blue}{-8x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)