Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+2}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+2}\color{blue}{-2-7x } & = & -12 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -12 \color{blue}{-2} \\\Leftrightarrow &-20x & = &-14\\\Leftrightarrow & \color{red}{-20}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-14}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-11}& = & -12 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11+4x } & = & -12 \color{red}{ -4x }\color{blue}{+11+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &13x & = &-1\\\Leftrightarrow & \color{red}{13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+13}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & -12 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-25\\\Leftrightarrow & \color{red}{-11}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-25}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{25}{11} } & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-10}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10-x } & = & 2 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+9}& = & -8 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9+8x } & = & -8 \color{red}{ -8x }\color{blue}{-9+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & -8 \color{blue}{-9} \\\Leftrightarrow &19x & = &-17\\\Leftrightarrow & \color{red}{19}x & = &-17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{19} } & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+7}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-x } & = & 4 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &-15x & = &-3\\\Leftrightarrow & \color{red}{-15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-3}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3-13x } & = & -1 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -1 \color{blue}{+3} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+13}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+13}\color{blue}{-13-9x } & = & -9 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-22\\\Leftrightarrow & \color{red}{-13}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+13}& = & 9 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13+6x } & = & 9 \color{red}{ -6x }\color{blue}{-13+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 9 \color{blue}{-13} \\\Leftrightarrow &19x & = &-4\\\Leftrightarrow & \color{red}{19}x & = &-4\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-4}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+8}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8-x } & = & 13 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 13 \color{blue}{-8} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+4}& = & -15 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4+13x } & = & -15 \color{red}{ -13x }\color{blue}{-4+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &20x & = &-19\\\Leftrightarrow & \color{red}{20}x & = &-19\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-19}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{20} } & & \\ & V = \left\{ \frac{-19}{20} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-14}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14-x } & = & -13 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)