Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-2}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2-x } & = & -4 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -4 \color{blue}{+2} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+2}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-x } & = & 14 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &-9x & = &12\\\Leftrightarrow & \color{red}{-9}x & = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+6}& = & -12 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6+10x } & = & -12 \color{red}{ -10x }\color{blue}{-6+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &21x & = &-18\\\Leftrightarrow & \color{red}{21}x & = &-18\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-18}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-8}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8-11x } & = & 10 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &-x & = &18\\\Leftrightarrow & \color{red}{-}x & = &18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{18}{-1} \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+4}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4-13x } & = & -9 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & -9 \color{blue}{-4} \\\Leftrightarrow &-8x & = &-13\\\Leftrightarrow & \color{red}{-8}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{8} } & & \\ & V = \left\{ \frac{13}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+11}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11-13x } & = & 5 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 5 \color{blue}{-11} \\\Leftrightarrow &-10x & = &-6\\\Leftrightarrow & \color{red}{-10}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-13}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-7x } & = & 13 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &-5x & = &26\\\Leftrightarrow & \color{red}{-5}x & = &26\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{26}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{5} } & & \\ & V = \left\{ \frac{-26}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-2}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-2}\color{blue}{+2-7x } & = & -12 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -12 \color{blue}{+2} \\\Leftrightarrow &-16x & = &-10\\\Leftrightarrow & \color{red}{-16}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-8}& = & 11 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8+3x } & = & 11 \color{red}{ -3x }\color{blue}{+8+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 11 \color{blue}{+8} \\\Leftrightarrow &13x & = &19\\\Leftrightarrow & \color{red}{13}x & = &19\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{19}{13} \\\Leftrightarrow & \color{green}{ x = \frac{19}{13} } & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+1}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x } & = & -4 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+11}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-7x } & = & -8 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-20x & = &-19\\\Leftrightarrow & \color{red}{-20}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-19}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{19}{20} } & & \\ & V = \left\{ \frac{19}{20} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-11}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-11}\color{blue}{+11-x } & = & 1 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 1 \color{blue}{+11} \\\Leftrightarrow &5x & = &12\\\Leftrightarrow & \color{red}{5}x & = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)