Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+12}& = & 1 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12+5x } & = & 1 \color{red}{ -5x }\color{blue}{-12+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 1 \color{blue}{-12} \\\Leftrightarrow &11x & = &-11\\\Leftrightarrow & \color{red}{11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-11}{11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-8}& = & 15 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8+6x } & = & 15 \color{red}{ -6x }\color{blue}{+8+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &13x & = &23\\\Leftrightarrow & \color{red}{13}x & = &23\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{23}{13} \\\Leftrightarrow & \color{green}{ x = \frac{23}{13} } & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-11}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11-x } & = & -9 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -9 \color{blue}{+11} \\\Leftrightarrow &13x & = &2\\\Leftrightarrow & \color{red}{13}x & = &2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-3}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-x } & = & 11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 11 \color{blue}{+3} \\\Leftrightarrow &-6x & = &14\\\Leftrightarrow & \color{red}{-6}x & = &14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2-x } & = & -11 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -11 \color{blue}{+2} \\\Leftrightarrow &-15x & = &-9\\\Leftrightarrow & \color{red}{-15}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+7}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7-x } & = & -4 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -4 \color{blue}{-7} \\\Leftrightarrow &5x & = &-11\\\Leftrightarrow & \color{red}{5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+4}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-7x } & = & 12 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &-20x & = &8\\\Leftrightarrow & \color{red}{-20}x & = &8\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{8}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+12}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-5x } & = & -15 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &-7x & = &-27\\\Leftrightarrow & \color{red}{-7}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-27}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{27}{7} } & & \\ & V = \left\{ \frac{27}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-5}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-x } & = & 15 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 15 \color{blue}{+5} \\\Leftrightarrow &-9x & = &20\\\Leftrightarrow & \color{red}{-9}x & = &20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{9} } & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+8}& = & 14 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8+8x } & = & 14 \color{red}{ -8x }\color{blue}{-8+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &17x & = &6\\\Leftrightarrow & \color{red}{17}x & = &6\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{6}{17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-5}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-7x } & = & 14 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &-13x & = &19\\\Leftrightarrow & \color{red}{-13}x & = &19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-x } & = & -3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)