Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{-9}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-x } & = & 4 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &-15x & = &13\\\Leftrightarrow & \color{red}{-15}x & = &13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-x } & = & -9 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &-10x & = &-19\\\Leftrightarrow & \color{red}{-10}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+4}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-x } & = & -5 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+13}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13+2x } & = & 2 \color{red}{ -2x }\color{blue}{-13+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 2 \color{blue}{-13} \\\Leftrightarrow &13x & = &-11\\\Leftrightarrow & \color{red}{13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+11}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11-x } & = & -13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -13 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-24\\\Leftrightarrow & \color{red}{-13}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-24}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{24}{13} } & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{+13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-x } & = & -14 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -14 \color{blue}{-13} \\\Leftrightarrow &-8x & = &-27\\\Leftrightarrow & \color{red}{-8}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-27}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{27}{8} } & & \\ & V = \left\{ \frac{27}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+14}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & -1 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-15\\\Leftrightarrow & \color{red}{-9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-14}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & -5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{+14} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-x } & = & -14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -14 \color{blue}{+13} \\\Leftrightarrow &-12x & = &-1\\\Leftrightarrow & \color{red}{-12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-11}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11-13x } & = & 7 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &-4x & = &18\\\Leftrightarrow & \color{red}{-4}x & = &18\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{18}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-12}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-x } & = & 11 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 11 \color{blue}{+12} \\\Leftrightarrow &-16x & = &23\\\Leftrightarrow & \color{red}{-16}x & = &23\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{23}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{16} } & & \\ & V = \left\{ \frac{-23}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+9}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-x } & = & 1 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 1 \color{blue}{-9} \\\Leftrightarrow &-10x & = &-8\\\Leftrightarrow & \color{red}{-10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)