Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-12}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12-13x } & = & -10 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &-x & = &2\\\Leftrightarrow & \color{red}{-}x & = &2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{2}{-1} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-x } & = & 2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &-8x & = &7\\\Leftrightarrow & \color{red}{-8}x & = &7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-13}& = & -15 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13+5x } & = & -15 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -15 \color{blue}{+13} \\\Leftrightarrow &16x & = &-2\\\Leftrightarrow & \color{red}{16}x & = &-2\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-2}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-7}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7+13x } & = & -14 \color{red}{ -13x }\color{blue}{+7+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -14 \color{blue}{+7} \\\Leftrightarrow &24x & = &-7\\\Leftrightarrow & \color{red}{24}x & = &-7\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-7}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{24} } & & \\ & V = \left\{ \frac{-7}{24} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+1}& = & 11 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+1}\color{blue}{-1-10x } & = & 11 \color{red}{ +10x }\color{blue}{-1-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 11 \color{blue}{-1} \\\Leftrightarrow &-13x & = &10\\\Leftrightarrow & \color{red}{-13}x & = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-10}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10+7x } & = & 15 \color{red}{ -7x }\color{blue}{+10+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &11x & = &25\\\Leftrightarrow & \color{red}{11}x & = &25\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{25}{11} \\\Leftrightarrow & \color{green}{ x = \frac{25}{11} } & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+4}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4-x } & = & -11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -11 \color{blue}{-4} \\\Leftrightarrow &11x & = &-15\\\Leftrightarrow & \color{red}{11}x & = &-15\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-15}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-14}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14-x } & = & 2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &-7x & = &16\\\Leftrightarrow & \color{red}{-7}x & = &16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+5}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & -13 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -13 \color{blue}{-5} \\\Leftrightarrow &-12x & = &-18\\\Leftrightarrow & \color{red}{-12}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-18}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-7}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7-9x } & = & -13 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -13 \color{blue}{+7} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+5}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-x } & = & -3 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &-4x & = &-8\\\Leftrightarrow & \color{red}{-4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-8}{-4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+15}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15-11x } & = & -8 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-23\\\Leftrightarrow & \color{red}{-5}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{23}{5} } & & \\ & V = \left\{ \frac{23}{5} \right\} & \\\end{align}\)