Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+8}& = & 9 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8-6x } & = & 9 \color{red}{ +6x }\color{blue}{-8-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 9 \color{blue}{-8} \\\Leftrightarrow &-x & = &1\\\Leftrightarrow & \color{red}{-}x & = &1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{1}{-1} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10-x } & = & -15 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &13x & = &-5\\\Leftrightarrow & \color{red}{13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+7}& = & -9 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7-6x } & = & -9 \color{red}{ +6x }\color{blue}{-7-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & -9 \color{blue}{-7} \\\Leftrightarrow &-x & = &-16\\\Leftrightarrow & \color{red}{-}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-16}{-1} \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-5}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5-13x } & = & 14 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &-28x & = &19\\\Leftrightarrow & \color{red}{-28}x & = &19\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{19}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{28} } & & \\ & V = \left\{ \frac{-19}{28} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+11}& = & -2 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11+9x } & = & -2 \color{red}{ -9x }\color{blue}{-11+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & -2 \color{blue}{-11} \\\Leftrightarrow &16x & = &-13\\\Leftrightarrow & \color{red}{16}x & = &-13\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-13}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{16} } & & \\ & V = \left\{ \frac{-13}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-5}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5-13x } & = & -11 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -11 \color{blue}{+5} \\\Leftrightarrow &-4x & = &-6\\\Leftrightarrow & \color{red}{-4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2-x } & = & -10 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &-6x & = &-12\\\Leftrightarrow & \color{red}{-6}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-12}{-6} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+6}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-x } & = & -13 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -13 \color{blue}{-6} \\\Leftrightarrow &-16x & = &-19\\\Leftrightarrow & \color{red}{-16}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-19}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{19}{16} } & & \\ & V = \left\{ \frac{19}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+10}& = & -9 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-8x } & = & -9 \color{red}{ +8x }\color{blue}{-10-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &-23x & = &-19\\\Leftrightarrow & \color{red}{-23}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-19}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{19}{23} } & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+7}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7-3x } & = & 11 \color{red}{ +3x }\color{blue}{-7-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1-x } & = & 6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-6x & = &5\\\Leftrightarrow & \color{red}{-6}x & = &5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-5}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-x } & = & -12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -12 \color{blue}{+5} \\\Leftrightarrow &-10x & = &-7\\\Leftrightarrow & \color{red}{-10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)