Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+14}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-13x } & = & -15 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -15 \color{blue}{-14} \\\Leftrightarrow &-25x & = &-29\\\Leftrightarrow & \color{red}{-25}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-29}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{29}{25} } & & \\ & V = \left\{ \frac{29}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+3}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3-x } & = & 15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &-5x & = &12\\\Leftrightarrow & \color{red}{-5}x & = &12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+13}& = & 6 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13-3x } & = & 6 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & 13x \color{blue}{-3x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &10x & = &-7\\\Leftrightarrow & \color{red}{10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-7}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-x } & = & 3 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+10}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10-x } & = & 10 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 10 \color{blue}{-10} \\\Leftrightarrow &9x & = &0\\\Leftrightarrow & \color{red}{9}x & = &0\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{0}{9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-12}& = & -9 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+14x } & = & -9 \color{red}{ -14x }\color{blue}{+12+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -9 \color{blue}{+12} \\\Leftrightarrow &17x & = &3\\\Leftrightarrow & \color{red}{17}x & = &3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-x } & = & 12 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 12 \color{blue}{-12} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-12}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12-x } & = & -1 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -1 \color{blue}{+12} \\\Leftrightarrow &-11x & = &11\\\Leftrightarrow & \color{red}{-11}x & = &11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{11}{-11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+12}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12+13x } & = & -14 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -14 \color{blue}{-12} \\\Leftrightarrow &23x & = &-26\\\Leftrightarrow & \color{red}{23}x & = &-26\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-26}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{23} } & & \\ & V = \left\{ \frac{-26}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+14}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-7x } & = & 2 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-12\\\Leftrightarrow & \color{red}{-13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-11}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-x } & = & 7 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &-6x & = &18\\\Leftrightarrow & \color{red}{-6}x & = &18\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{18}{-6} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+11}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11-x } & = & 8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 8 \color{blue}{-11} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)