Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-9}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9-x } & = & 1 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &13x & = &10\\\Leftrightarrow & \color{red}{13}x & = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-1}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1-x } & = & -9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -9 \color{blue}{+1} \\\Leftrightarrow &x & = &-8\\\Leftrightarrow & \color{red}{}x & = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+12}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12-13x } & = & 11 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-x } & = & -8 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -8 \color{blue}{+14} \\\Leftrightarrow &-8x & = &6\\\Leftrightarrow & \color{red}{-8}x & = &6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-6}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-x } & = & 5 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{+6} \\\Leftrightarrow &-6x & = &11\\\Leftrightarrow & \color{red}{-6}x & = &11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+3}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3-5x } & = & 4 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 9x \color{blue}{-5x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &4x & = &1\\\Leftrightarrow & \color{red}{4}x & = &1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+4}& = & -12 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4+2x } & = & -12 \color{red}{ -2x }\color{blue}{-4+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -12 \color{blue}{-4} \\\Leftrightarrow &5x & = &-16\\\Leftrightarrow & \color{red}{5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-13}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13-x } & = & 13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &12x & = &26\\\Leftrightarrow & \color{red}{12}x & = &26\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{26}{12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+5}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5-7x } & = & -3 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &3x & = &-8\\\Leftrightarrow & \color{red}{3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-7}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-9x } & = & -5 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & -5 \color{blue}{+7} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+6}& = & -9 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6+2x } & = & -9 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &13x & = &-15\\\Leftrightarrow & \color{red}{13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-3}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3+11x } & = & 7 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 7 \color{blue}{+3} \\\Leftrightarrow &17x & = &10\\\Leftrightarrow & \color{red}{17}x & = &10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)