Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+14}& = & 5 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14+11x } & = & 5 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 5 \color{blue}{-14} \\\Leftrightarrow &17x & = &-9\\\Leftrightarrow & \color{red}{17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{17} } & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+10}& = & 12 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10+4x } & = & 12 \color{red}{ -4x }\color{blue}{-10+4x } \\\Leftrightarrow & x \color{blue}{+4x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+13}& = & -1 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13+4x } & = & -1 \color{red}{ -4x }\color{blue}{-13+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &13x & = &-14\\\Leftrightarrow & \color{red}{13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-7}& = & 9 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7+5x } & = & 9 \color{red}{ -5x }\color{blue}{+7+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 9 \color{blue}{+7} \\\Leftrightarrow &11x & = &16\\\Leftrightarrow & \color{red}{11}x & = &16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+15}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15-13x } & = & -1 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &-9x & = &-16\\\Leftrightarrow & \color{red}{-9}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-13}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-x } & = & -3 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -3 \color{blue}{+13} \\\Leftrightarrow &-11x & = &10\\\Leftrightarrow & \color{red}{-11}x & = &10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+6}& = & -13 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6+2x } & = & -13 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & -13 \color{blue}{-6} \\\Leftrightarrow &11x & = &-19\\\Leftrightarrow & \color{red}{11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-19}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{11} } & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-7}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-11x } & = & -2 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &-21x & = &5\\\Leftrightarrow & \color{red}{-21}x & = &5\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{5}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{21} } & & \\ & V = \left\{ \frac{-5}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-13}& = & 15 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13+15x } & = & 15 \color{red}{ -15x }\color{blue}{+13+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &28x & = &28\\\Leftrightarrow & \color{red}{28}x & = &28\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{28}{28} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-6}& = & -13 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6+2x } & = & -13 \color{red}{ -2x }\color{blue}{+6+2x } \\\Leftrightarrow & 7x \color{blue}{+2x } & = & -13 \color{blue}{+6} \\\Leftrightarrow &9x & = &-7\\\Leftrightarrow & \color{red}{9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-7}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-4}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4-11x } & = & -11 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & -11 \color{blue}{+4} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+6}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6-13x } & = & -4 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -4 \color{blue}{-6} \\\Leftrightarrow &-4x & = &-10\\\Leftrightarrow & \color{red}{-4}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)