Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+10}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10-9x } & = & -15 \color{red}{ +9x }\color{blue}{-10-9x } \\\Leftrightarrow & 11x \color{blue}{-9x } & = & -15 \color{blue}{-10} \\\Leftrightarrow &2x & = &-25\\\Leftrightarrow & \color{red}{2}x & = &-25\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-25}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{2} } & & \\ & V = \left\{ \frac{-25}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-13}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13-7x } & = & -13 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -13 \color{blue}{+13} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+9}& = & 3 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9-6x } & = & 3 \color{red}{ +6x }\color{blue}{-9-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & 3 \color{blue}{-9} \\\Leftrightarrow &7x & = &-6\\\Leftrightarrow & \color{red}{7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-11}& = & 9 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-6x } & = & 9 \color{red}{ +6x }\color{blue}{+11-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &-11x & = &20\\\Leftrightarrow & \color{red}{-11}x & = &20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+12}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-x } & = & 1 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 1 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-11\\\Leftrightarrow & \color{red}{-3}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+7}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-x } & = & -13 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &-9x & = &-20\\\Leftrightarrow & \color{red}{-9}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{20}{9} } & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+3}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3-11x } & = & -9 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -9 \color{blue}{-3} \\\Leftrightarrow &-9x & = &-12\\\Leftrightarrow & \color{red}{-9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+15}& = & -13 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15-2x } & = & -13 \color{red}{ +2x }\color{blue}{-15-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &13x & = &-28\\\Leftrightarrow & \color{red}{13}x & = &-28\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-28}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{13} } & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-9}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9-13x } & = & -10 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+6}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-x } & = & -13 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -13 \color{blue}{-6} \\\Leftrightarrow &-6x & = &-19\\\Leftrightarrow & \color{red}{-6}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{19}{6} } & & \\ & V = \left\{ \frac{19}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-8}& = & -14 \color{red}{ +14x } \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8-14x } & = & -14 \color{red}{ +14x }\color{blue}{+8-14x } \\\Leftrightarrow & 9x \color{blue}{-14x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &-5x & = &-6\\\Leftrightarrow & \color{red}{-5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-x } & = & -7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)