Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-13}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13-13x } & = & 6 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 6 \color{blue}{+13} \\\Leftrightarrow &-25x & = &19\\\Leftrightarrow & \color{red}{-25}x & = &19\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{19}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{25} } & & \\ & V = \left\{ \frac{-19}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+4}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-x } & = & 1 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 1 \color{blue}{-4} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+4}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4+13x } & = & -10 \color{red}{ -13x }\color{blue}{-4+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &20x & = &-14\\\Leftrightarrow & \color{red}{20}x & = &-14\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-14}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+6}& = & -3 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6+3x } & = & -3 \color{red}{ -3x }\color{blue}{-6+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &7x & = &-9\\\Leftrightarrow & \color{red}{7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+4}& = & -8 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-3x } & = & -8 \color{red}{ +3x }\color{blue}{-4-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &-11x & = &-12\\\Leftrightarrow & \color{red}{-11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+15}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-7x } & = & 13 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 13 \color{blue}{-15} \\\Leftrightarrow &-10x & = &-2\\\Leftrightarrow & \color{red}{-10}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-13}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13-x } & = & 9 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 9 \color{blue}{+13} \\\Leftrightarrow &-16x & = &22\\\Leftrightarrow & \color{red}{-16}x & = &22\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{22}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-9}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-9x } & = & -5 \color{red}{ +9x }\color{blue}{+9-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -5 \color{blue}{+9} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+12}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12-7x } & = & 12 \color{red}{ +7x }\color{blue}{-12-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 12 \color{blue}{-12} \\\Leftrightarrow &-20x & = &0\\\Leftrightarrow & \color{red}{-20}x & = &0\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{0}{-20} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+8}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8-x } & = & 14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-16x & = &6\\\Leftrightarrow & \color{red}{-16}x & = &6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+11}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-x } & = & 6 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &-4x & = &-5\\\Leftrightarrow & \color{red}{-4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-6}& = & -9 \color{red}{ +14x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6-14x } & = & -9 \color{red}{ +14x }\color{blue}{+6-14x } \\\Leftrightarrow & 5x \color{blue}{-14x } & = & -9 \color{blue}{+6} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)