Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13-x } & = & 11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &13x & = &24\\\Leftrightarrow & \color{red}{13}x & = &24\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{24}{13} \\\Leftrightarrow & \color{green}{ x = \frac{24}{13} } & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-11}& = & 10 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11-4x } & = & 10 \color{red}{ +4x }\color{blue}{+11-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &-11x & = &21\\\Leftrightarrow & \color{red}{-11}x & = &21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+3}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3-3x } & = & 4 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & 7x \color{blue}{-3x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &4x & = &1\\\Leftrightarrow & \color{red}{4}x & = &1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+9}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9-7x } & = & -13 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &-4x & = &-22\\\Leftrightarrow & \color{red}{-4}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-22}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-x } & = & -10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -10 \color{blue}{-3} \\\Leftrightarrow &-7x & = &-13\\\Leftrightarrow & \color{red}{-7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-8}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8-13x } & = & 14 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 14 \color{blue}{+8} \\\Leftrightarrow &-10x & = &22\\\Leftrightarrow & \color{red}{-10}x & = &22\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{22}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+13}& = & 15 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13+5x } & = & 15 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &8x & = &2\\\Leftrightarrow & \color{red}{8}x & = &2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-8}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-5x } & = & 8 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &9x & = &16\\\Leftrightarrow & \color{red}{9}x & = &16\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{16}{9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+7}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7-11x } & = & -15 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -15 \color{blue}{-7} \\\Leftrightarrow &-5x & = &-22\\\Leftrightarrow & \color{red}{-5}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+14}& = & -4 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14+12x } & = & -4 \color{red}{ -12x }\color{blue}{-14+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &25x & = &-18\\\Leftrightarrow & \color{red}{25}x & = &-18\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-18}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{25} } & & \\ & V = \left\{ \frac{-18}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-10x & = &-5\\\Leftrightarrow & \color{red}{-10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-13}& = & 7 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13+8x } & = & 7 \color{red}{ -8x }\color{blue}{+13+8x } \\\Leftrightarrow & -x \color{blue}{+8x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &7x & = &20\\\Leftrightarrow & \color{red}{7}x & = &20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{20}{7} } & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)