Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+8}& = & 4 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8+9x } & = & 4 \color{red}{ -9x }\color{blue}{-8+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & 4 \color{blue}{-8} \\\Leftrightarrow &16x & = &-4\\\Leftrightarrow & \color{red}{16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-4}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+8}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8-13x } & = & -3 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-5}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5-7x } & = & -11 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -11 \color{blue}{+5} \\\Leftrightarrow &-20x & = &-6\\\Leftrightarrow & \color{red}{-20}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-6}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-8}& = & 2 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8-3x } & = & 2 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &7x & = &10\\\Leftrightarrow & \color{red}{7}x & = &10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+12}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12-13x } & = & 15 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &-16x & = &3\\\Leftrightarrow & \color{red}{-16}x & = &3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{16} } & & \\ & V = \left\{ \frac{-3}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-6}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6-13x } & = & -2 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & -2 \color{blue}{+6} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-x } & = & -8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &-6x & = &-20\\\Leftrightarrow & \color{red}{-6}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-20}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-x } & = & 12 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &-11x & = &27\\\Leftrightarrow & \color{red}{-11}x & = &27\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{27}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{11} } & & \\ & V = \left\{ \frac{-27}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+4}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-3x } & = & -5 \color{red}{ +3x }\color{blue}{-4-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-5}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x } & = & 15 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 15 \color{blue}{+5} \\\Leftrightarrow &-13x & = &20\\\Leftrightarrow & \color{red}{-13}x & = &20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{13} } & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6-x } & = & 9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &4x & = &3\\\Leftrightarrow & \color{red}{4}x & = &3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-10}& = & -8 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10+14x } & = & -8 \color{red}{ -14x }\color{blue}{+10+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &29x & = &2\\\Leftrightarrow & \color{red}{29}x & = &2\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{2}{29} \\\Leftrightarrow & \color{green}{ x = \frac{2}{29} } & & \\ & V = \left\{ \frac{2}{29} \right\} & \\\end{align}\)