Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-7}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-11x } & = & 10 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &-13x & = &17\\\Leftrightarrow & \color{red}{-13}x & = &17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+14}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14-11x } & = & -2 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-16\\\Leftrightarrow & \color{red}{-7}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+3}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-13x } & = & 10 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 10 \color{blue}{-3} \\\Leftrightarrow &-25x & = &7\\\Leftrightarrow & \color{red}{-25}x & = &7\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{7}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{25} } & & \\ & V = \left\{ \frac{-7}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+15}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-x } & = & 5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-10\\\Leftrightarrow & \color{red}{-5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-7}& = & 11 \color{red}{ -14x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7+14x } & = & 11 \color{red}{ -14x }\color{blue}{+7+14x } \\\Leftrightarrow & -x \color{blue}{+14x } & = & 11 \color{blue}{+7} \\\Leftrightarrow &13x & = &18\\\Leftrightarrow & \color{red}{13}x & = &18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+9}& = & -2 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9+13x } & = & -2 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &20x & = &-11\\\Leftrightarrow & \color{red}{20}x & = &-11\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-11}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{20} } & & \\ & V = \left\{ \frac{-11}{20} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-9}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-9}\color{blue}{+9-x } & = & -3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -3 \color{blue}{+9} \\\Leftrightarrow &2x & = &6\\\Leftrightarrow & \color{red}{2}x & = &6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{6}{2} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{-15}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15-x } & = & 9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &-4x & = &24\\\Leftrightarrow & \color{red}{-4}x & = &24\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{24}{-4} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+2}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2+7x } & = & -4 \color{red}{ -7x }\color{blue}{-2+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &12x & = &-6\\\Leftrightarrow & \color{red}{12}x & = &-6\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-6}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+6}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6-x } & = & -13 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -13 \color{blue}{-6} \\\Leftrightarrow &10x & = &-19\\\Leftrightarrow & \color{red}{10}x & = &-19\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-19}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{10} } & & \\ & V = \left\{ \frac{-19}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+11}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-9x } & = & 3 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &-17x & = &-8\\\Leftrightarrow & \color{red}{-17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+1}& = & -9 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-4x } & = & -9 \color{red}{ +4x }\color{blue}{-1-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &-19x & = &-10\\\Leftrightarrow & \color{red}{-19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-10}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)