Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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