Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+5}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5-x } & = & 9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 9 \color{blue}{-5} \\\Leftrightarrow &5x & = &4\\\Leftrightarrow & \color{red}{5}x & = &4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{-10}& = & 10 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10+12x } & = & 10 \color{red}{ -12x }\color{blue}{+10+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 10 \color{blue}{+10} \\\Leftrightarrow &25x & = &20\\\Leftrightarrow & \color{red}{25}x & = &20\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{20}{25} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-x } & = & 2 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 2 \color{blue}{-5} \\\Leftrightarrow &-4x & = &-3\\\Leftrightarrow & \color{red}{-4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+4}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4-13x } & = & -13 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & -13 \color{blue}{-4} \\\Leftrightarrow &-2x & = &-17\\\Leftrightarrow & \color{red}{-2}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-17}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{17}{2} } & & \\ & V = \left\{ \frac{17}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+5}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-x } & = & 15 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &-3x & = &10\\\Leftrightarrow & \color{red}{-3}x & = &10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+13}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-5x } & = & -15 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &-17x & = &-28\\\Leftrightarrow & \color{red}{-17}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-28}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{28}{17} } & & \\ & V = \left\{ \frac{28}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-x } & = & -3 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &-16x & = &-9\\\Leftrightarrow & \color{red}{-16}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-9}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{9}{16} } & & \\ & V = \left\{ \frac{9}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-13}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13-x } & = & -2 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{+13} \\\Leftrightarrow &-15x & = &11\\\Leftrightarrow & \color{red}{-15}x & = &11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+14}& = & -9 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14-2x } & = & -9 \color{red}{ +2x }\color{blue}{-14-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & -9 \color{blue}{-14} \\\Leftrightarrow &13x & = &-23\\\Leftrightarrow & \color{red}{13}x & = &-23\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-23}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{13} } & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-15}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15-5x } & = & -5 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -5 \color{blue}{+15} \\\Leftrightarrow &x & = &10\\\Leftrightarrow & \color{red}{}x & = &10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 10 \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-6}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-13x } & = & -5 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &-25x & = &1\\\Leftrightarrow & \color{red}{-25}x & = &1\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{1}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{25} } & & \\ & V = \left\{ \frac{-1}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-11}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-11}\color{blue}{+11-5x } & = & -3 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & -3 \color{blue}{+11} \\\Leftrightarrow &-x & = &8\\\Leftrightarrow & \color{red}{-}x & = &8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{8}{-1} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)