Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-x } & = & 9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 9 \color{blue}{+9} \\\Leftrightarrow &-3x & = &18\\\Leftrightarrow & \color{red}{-3}x & = &18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{18}{-3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+13}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13+11x } & = & -9 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &23x & = &-22\\\Leftrightarrow & \color{red}{23}x & = &-22\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-22}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{23} } & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+8}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8+11x } & = & 8 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 8 \color{blue}{-8} \\\Leftrightarrow &17x & = &0\\\Leftrightarrow & \color{red}{17}x & = &0\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{0}{17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+9}& = & -14 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-14x } & = & -14 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -14 \color{blue}{-9} \\\Leftrightarrow &-23x & = &-23\\\Leftrightarrow & \color{red}{-23}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-23}{-23} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-12}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-x } & = & -3 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -3 \color{blue}{+12} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-1}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1-13x } & = & 15 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &-16x & = &16\\\Leftrightarrow & \color{red}{-16}x & = &16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{16}{-16} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+7}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+7}\color{blue}{-7-x } & = & -12 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &-14x & = &-19\\\Leftrightarrow & \color{red}{-14}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{19}{14} } & & \\ & V = \left\{ \frac{19}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-1}& = & -11 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1+6x } & = & -11 \color{red}{ -6x }\color{blue}{+1+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -11 \color{blue}{+1} \\\Leftrightarrow &19x & = &-10\\\Leftrightarrow & \color{red}{19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+3}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-3x } & = & -3 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & -3 \color{blue}{-3} \\\Leftrightarrow &-8x & = &-6\\\Leftrightarrow & \color{red}{-8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{-13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13-x } & = & 10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &-16x & = &23\\\Leftrightarrow & \color{red}{-16}x & = &23\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{23}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{16} } & & \\ & V = \left\{ \frac{-23}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15-x } & = & -2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-6}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6-x } & = & 8 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &-11x & = &14\\\Leftrightarrow & \color{red}{-11}x & = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)