Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-12}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12-13x } & = & 10 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -x \color{blue}{-13x } & = & 10 \color{blue}{+12} \\\Leftrightarrow &-14x & = &22\\\Leftrightarrow & \color{red}{-14}x & = &22\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{22}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+3}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3-13x } & = & -6 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -6 \color{blue}{-3} \\\Leftrightarrow &-x & = &-9\\\Leftrightarrow & \color{red}{-}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-9}{-1} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-13}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-x } & = & -10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -10 \color{blue}{+13} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-1}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1-13x } & = & 1 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 1 \color{blue}{+1} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+14}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-13x } & = & -12 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &-25x & = &-26\\\Leftrightarrow & \color{red}{-25}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-26}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{26}{25} } & & \\ & V = \left\{ \frac{26}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+14}& = & -10 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14+2x } & = & -10 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -10 \color{blue}{-14} \\\Leftrightarrow &17x & = &-24\\\Leftrightarrow & \color{red}{17}x & = &-24\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-24}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{17} } & & \\ & V = \left\{ \frac{-24}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-10}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-x } & = & 11 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &-3x & = &21\\\Leftrightarrow & \color{red}{-3}x & = &21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{21}{-3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+6}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6+2x } & = & -2 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &5x & = &-8\\\Leftrightarrow & \color{red}{5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-10}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-7x } & = & -8 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &-17x & = &2\\\Leftrightarrow & \color{red}{-17}x & = &2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-7}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7+11x } & = & -8 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &23x & = &-1\\\Leftrightarrow & \color{red}{23}x & = &-1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-x } & = & -3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-6}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-x } & = & -6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &-16x & = &0\\\Leftrightarrow & \color{red}{-16}x & = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)