Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-9}& = & 10 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9+3x } & = & 10 \color{red}{ -3x }\color{blue}{+9+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &7x & = &19\\\Leftrightarrow & \color{red}{7}x & = &19\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{19}{7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-11}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-13x } & = & 8 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 8 \color{blue}{+11} \\\Leftrightarrow &-17x & = &19\\\Leftrightarrow & \color{red}{-17}x & = &19\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{19}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{17} } & & \\ & V = \left\{ \frac{-19}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-11}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-13x } & = & 3 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &-17x & = &14\\\Leftrightarrow & \color{red}{-17}x & = &14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+3}& = & -3 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3-10x } & = & -3 \color{red}{ +10x }\color{blue}{-3-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -3 \color{blue}{-3} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+3}& = & -8 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3+10x } & = & -8 \color{red}{ -10x }\color{blue}{-3+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -8 \color{blue}{-3} \\\Leftrightarrow &17x & = &-11\\\Leftrightarrow & \color{red}{17}x & = &-11\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-11}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{17} } & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-12}& = & 8 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12+9x } & = & 8 \color{red}{ -9x }\color{blue}{+12+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 8 \color{blue}{+12} \\\Leftrightarrow &14x & = &20\\\Leftrightarrow & \color{red}{14}x & = &20\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{20}{14} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+2}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & -8 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -8 \color{blue}{-2} \\\Leftrightarrow &-15x & = &-10\\\Leftrightarrow & \color{red}{-15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-5}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x } & = & 10 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 10 \color{blue}{+5} \\\Leftrightarrow &-13x & = &15\\\Leftrightarrow & \color{red}{-13}x & = &15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-14}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-9x } & = & 12 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 12 \color{blue}{+14} \\\Leftrightarrow &-20x & = &26\\\Leftrightarrow & \color{red}{-20}x & = &26\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{26}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-9}& = & 6 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9+13x } & = & 6 \color{red}{ -13x }\color{blue}{+9+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &23x & = &15\\\Leftrightarrow & \color{red}{23}x & = &15\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{15}{23} \\\Leftrightarrow & \color{green}{ x = \frac{15}{23} } & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-8}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-13x } & = & -13 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &-17x & = &-5\\\Leftrightarrow & \color{red}{-17}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-5}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{5}{17} } & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+6}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-x } & = & -5 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)