Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+13}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-x } & = & 14 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 14 \color{blue}{-13} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-x } & = & -8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-23\\\Leftrightarrow & \color{red}{-13}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-23}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{23}{13} } & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-14}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14+13x } & = & -3 \color{red}{ -13x }\color{blue}{+14+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &20x & = &11\\\Leftrightarrow & \color{red}{20}x & = &11\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{11}{20} \\\Leftrightarrow & \color{green}{ x = \frac{11}{20} } & & \\ & V = \left\{ \frac{11}{20} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-x } & = & 7 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{-13} \\\Leftrightarrow &-9x & = &-6\\\Leftrightarrow & \color{red}{-9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-15}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15-x } & = & -5 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -5 \color{blue}{+15} \\\Leftrightarrow &x & = &10\\\Leftrightarrow & \color{red}{}x & = &10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 10 \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-6}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-6}\color{blue}{+6-5x } & = & -3 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+11}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-x } & = & -1 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &-6x & = &-12\\\Leftrightarrow & \color{red}{-6}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-12}{-6} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+8}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8-5x } & = & 2 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-9}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-x } & = & 5 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 5 \color{blue}{+9} \\\Leftrightarrow &-4x & = &14\\\Leftrightarrow & \color{red}{-4}x & = &14\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{14}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-5}& = & -7 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5+13x } & = & -7 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &24x & = &-2\\\Leftrightarrow & \color{red}{24}x & = &-2\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-2}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-2}& = & 7 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2+3x } & = & 7 \color{red}{ -3x }\color{blue}{+2+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &10x & = &9\\\Leftrightarrow & \color{red}{10}x & = &9\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{9}{10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+7}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7+13x } & = & -11 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &27x & = &-18\\\Leftrightarrow & \color{red}{27}x & = &-18\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-18}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)