Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+14}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-7x } & = & -6 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &-17x & = &-20\\\Leftrightarrow & \color{red}{-17}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-20}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{20}{17} } & & \\ & V = \left\{ \frac{20}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-14}& = & -1 \color{red}{ +2x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14-2x } & = & -1 \color{red}{ +2x }\color{blue}{+14-2x } \\\Leftrightarrow & 3x \color{blue}{-2x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &x & = &13\\\Leftrightarrow & \color{red}{}x & = &13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 13 \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+9}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & -5 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-14\\\Leftrightarrow & \color{red}{-9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-13}& = & -9 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-13}\color{blue}{+13+3x } & = & -9 \color{red}{ -3x }\color{blue}{+13+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -9 \color{blue}{+13} \\\Leftrightarrow &10x & = &4\\\Leftrightarrow & \color{red}{10}x & = &4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-7}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-x } & = & 9 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 9 \color{blue}{+7} \\\Leftrightarrow &-14x & = &16\\\Leftrightarrow & \color{red}{-14}x & = &16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+6}& = & -5 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6+3x } & = & -5 \color{red}{ -3x }\color{blue}{-6+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &10x & = &-11\\\Leftrightarrow & \color{red}{10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-9}& = & -6 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9-9x } & = & -6 \color{red}{ +9x }\color{blue}{+9-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+6}& = & 1 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6+5x } & = & 1 \color{red}{ -5x }\color{blue}{-6+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &8x & = &-5\\\Leftrightarrow & \color{red}{8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-x } & = & 4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+12}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-9x } & = & 6 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 6 \color{blue}{-12} \\\Leftrightarrow &-17x & = &-6\\\Leftrightarrow & \color{red}{-17}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11-x } & = & 12 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+9}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-x } & = & -6 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-15\\\Leftrightarrow & \color{red}{-5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-15}{-5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)