Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-7}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-9x } & = & -10 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & -10 \color{blue}{+7} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+5}& = & -5 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-10x } & = & -5 \color{red}{ +10x }\color{blue}{-5-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & -5 \color{blue}{-5} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x } & = & 13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-6x & = &18\\\Leftrightarrow & \color{red}{-6}x & = &18\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{18}{-6} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+6}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6-x } & = & -1 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+11}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11-x } & = & 9 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 9 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+5}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & 3 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &-15x & = &-2\\\Leftrightarrow & \color{red}{-15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-10}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-x } & = & 12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &-9x & = &22\\\Leftrightarrow & \color{red}{-9}x & = &22\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{22}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{9} } & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+8}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-7x } & = & 8 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 8 \color{blue}{-8} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-3}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3-3x } & = & 3 \color{red}{ +3x }\color{blue}{+3-3x } \\\Leftrightarrow & -x \color{blue}{-3x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &-4x & = &6\\\Leftrightarrow & \color{red}{-4}x & = &6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-13}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13-7x } & = & -10 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -10 \color{blue}{+13} \\\Leftrightarrow &3x & = &3\\\Leftrightarrow & \color{red}{3}x & = &3\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{3}{3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-13}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13-x } & = & 14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 14 \color{blue}{+13} \\\Leftrightarrow &-5x & = &27\\\Leftrightarrow & \color{red}{-5}x & = &27\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{27}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{5} } & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-11}& = & 11 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11+13x } & = & 11 \color{red}{ -13x }\color{blue}{+11+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 11 \color{blue}{+11} \\\Leftrightarrow &23x & = &22\\\Leftrightarrow & \color{red}{23}x & = &22\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{22}{23} \\\Leftrightarrow & \color{green}{ x = \frac{22}{23} } & & \\ & V = \left\{ \frac{22}{23} \right\} & \\\end{align}\)