Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+4}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-7x } & = & 14 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 14 \color{blue}{-4} \\\Leftrightarrow &-13x & = &10\\\Leftrightarrow & \color{red}{-13}x & = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+4}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-x } & = & 14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 14 \color{blue}{-4} \\\Leftrightarrow &-13x & = &10\\\Leftrightarrow & \color{red}{-13}x & = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-11}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11+13x } & = & -14 \color{red}{ -13x }\color{blue}{+11+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &27x & = &-3\\\Leftrightarrow & \color{red}{27}x & = &-3\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-3}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x } & = & 9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 9 \color{blue}{-1} \\\Leftrightarrow &-9x & = &8\\\Leftrightarrow & \color{red}{-9}x & = &8\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{8}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-9}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-9}\color{blue}{+9-x } & = & -12 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -12 \color{blue}{+9} \\\Leftrightarrow &2x & = &-3\\\Leftrightarrow & \color{red}{2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-8}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-8}\color{blue}{+8-11x } & = & 12 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &-3x & = &20\\\Leftrightarrow & \color{red}{-3}x & = &20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-13}& = & -3 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-10x } & = & -3 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & -3 \color{blue}{+13} \\\Leftrightarrow &-13x & = &10\\\Leftrightarrow & \color{red}{-13}x & = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+6}& = & 14 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6-9x } & = & 14 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 14 \color{blue}{-6} \\\Leftrightarrow &-20x & = &8\\\Leftrightarrow & \color{red}{-20}x & = &8\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{8}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-6}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6-x } & = & 4 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 4 \color{blue}{+6} \\\Leftrightarrow &4x & = &10\\\Leftrightarrow & \color{red}{4}x & = &10\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{10}{4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-13}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13-13x } & = & -9 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -9 \color{blue}{+13} \\\Leftrightarrow &-25x & = &4\\\Leftrightarrow & \color{red}{-25}x & = &4\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{4}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{25} } & & \\ & V = \left\{ \frac{-4}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-14}& = & -13 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-14x } & = & -13 \color{red}{ +14x }\color{blue}{+14-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &-23x & = &1\\\Leftrightarrow & \color{red}{-23}x & = &1\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{1}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+10}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-11x } & = & -3 \color{red}{ +11x }\color{blue}{-10-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &-13x & = &-13\\\Leftrightarrow & \color{red}{-13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)