Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+2}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+2}\color{blue}{-2-14x } & = & 12 \color{red}{ +14x }\color{blue}{-2-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &-27x & = &10\\\Leftrightarrow & \color{red}{-27}x & = &10\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{10}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{27} } & & \\ & V = \left\{ \frac{-10}{27} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+7}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7-13x } & = & 9 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+4}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-11x } & = & -12 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -12 \color{blue}{-4} \\\Leftrightarrow &-18x & = &-16\\\Leftrightarrow & \color{red}{-18}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-16}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-12}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12-x } & = & -12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -12 \color{blue}{+12} \\\Leftrightarrow &4x & = &0\\\Leftrightarrow & \color{red}{4}x & = &0\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{0}{4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-8}& = & -1 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8+2x } & = & -1 \color{red}{ -2x }\color{blue}{+8+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -1 \color{blue}{+8} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-13}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13-13x } & = & -15 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -15 \color{blue}{+13} \\\Leftrightarrow &-25x & = &-2\\\Leftrightarrow & \color{red}{-25}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-2}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{2}{25} } & & \\ & V = \left\{ \frac{2}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+12}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12-7x } & = & 12 \color{red}{ +7x }\color{blue}{-12-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 12 \color{blue}{-12} \\\Leftrightarrow &-20x & = &0\\\Leftrightarrow & \color{red}{-20}x & = &0\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{0}{-20} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-x } & = & -9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &-7x & = &-18\\\Leftrightarrow & \color{red}{-7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+14}& = & 2 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-3x } & = & 2 \color{red}{ +3x }\color{blue}{-14-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-9}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-x } & = & 15 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &-4x & = &24\\\Leftrightarrow & \color{red}{-4}x & = &24\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{24}{-4} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-13}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-x } & = & 5 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 5 \color{blue}{+13} \\\Leftrightarrow &-11x & = &18\\\Leftrightarrow & \color{red}{-11}x & = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+4}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4+13x } & = & -3 \color{red}{ -13x }\color{blue}{-4+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &27x & = &-7\\\Leftrightarrow & \color{red}{27}x & = &-7\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-7}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{27} } & & \\ & V = \left\{ \frac{-7}{27} \right\} & \\\end{align}\)