Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-5}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5-7x } & = & -2 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & -2 \color{blue}{+5} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{+6}& = & 12 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6+15x } & = & 12 \color{red}{ -15x }\color{blue}{-6+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & 12 \color{blue}{-6} \\\Leftrightarrow &28x & = &6\\\Leftrightarrow & \color{red}{28}x & = &6\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{6}{28} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+4}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4+13x } & = & 14 \color{red}{ -13x }\color{blue}{-4+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 14 \color{blue}{-4} \\\Leftrightarrow &20x & = &10\\\Leftrightarrow & \color{red}{20}x & = &10\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{10}{20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+4}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-x } & = & 15 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 15 \color{blue}{-4} \\\Leftrightarrow &-10x & = &11\\\Leftrightarrow & \color{red}{-10}x & = &11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-x } & = & 6 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-15}\color{blue}{+15-x } & = & 12 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &-15x & = &27\\\Leftrightarrow & \color{red}{-15}x & = &27\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{27}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-5}& = & 5 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5+13x } & = & 5 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 5 \color{blue}{+5} \\\Leftrightarrow &24x & = &10\\\Leftrightarrow & \color{red}{24}x & = &10\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{10}{24} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-2}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2-5x } & = & 2 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 2 \color{blue}{+2} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+9}& = & -3 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9+2x } & = & -3 \color{red}{ -2x }\color{blue}{-9+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -3 \color{blue}{-9} \\\Leftrightarrow &13x & = &-12\\\Leftrightarrow & \color{red}{13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-10}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10-13x } & = & 12 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &x & = &22\\\Leftrightarrow & \color{red}{}x & = &22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 22 \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-14}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14-13x } & = & -13 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-5}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-11x } & = & -1 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)