Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+2}& = & -4 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2-8x } & = & -4 \color{red}{ +8x }\color{blue}{-2-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-3}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3-13x } & = & -9 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6-x } & = & 7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &7x & = &1\\\Leftrightarrow & \color{red}{7}x & = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-10}& = & -10 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-4x } & = & -10 \color{red}{ +4x }\color{blue}{+10-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -10 \color{blue}{+10} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+3}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-x } & = & 1 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 1 \color{blue}{-3} \\\Leftrightarrow &-15x & = &-2\\\Leftrightarrow & \color{red}{-15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+4}& = & -3 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4+2x } & = & -3 \color{red}{ -2x }\color{blue}{-4+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &17x & = &-7\\\Leftrightarrow & \color{red}{17}x & = &-7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+6}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6-x } & = & -5 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &-4x & = &-11\\\Leftrightarrow & \color{red}{-4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-6}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6-7x } & = & 13 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -x \color{blue}{-7x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &-8x & = &19\\\Leftrightarrow & \color{red}{-8}x & = &19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{-10}& = & -1 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10-3x } & = & -1 \color{red}{ +3x }\color{blue}{+10-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-10}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-10}\color{blue}{+10-x } & = & -7 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &2x & = &3\\\Leftrightarrow & \color{red}{2}x & = &3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & 13 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{-9} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-6}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6-9x } & = & -12 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)