Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+2}& = & 10 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2+3x } & = & 10 \color{red}{ -3x }\color{blue}{-2+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 10 \color{blue}{-2} \\\Leftrightarrow &13x & = &8\\\Leftrightarrow & \color{red}{13}x & = &8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+11}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11-x } & = & -9 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -9 \color{blue}{-11} \\\Leftrightarrow &-12x & = &-20\\\Leftrightarrow & \color{red}{-12}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-20}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+12}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-5x } & = & 13 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 13 \color{blue}{-12} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+5}\color{blue}{-5-x } & = & 2 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 2 \color{blue}{-5} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{+12}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12-x } & = & 3 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 3 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+1}& = & -9 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1+12x } & = & -9 \color{red}{ -12x }\color{blue}{-1+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &25x & = &-10\\\Leftrightarrow & \color{red}{25}x & = &-10\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-10}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+13}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13-13x } & = & -8 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -8 \color{blue}{-13} \\\Leftrightarrow &-4x & = &-21\\\Leftrightarrow & \color{red}{-4}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-21}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{21}{4} } & & \\ & V = \left\{ \frac{21}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+7}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7-13x } & = & -8 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -8 \color{blue}{-7} \\\Leftrightarrow &-25x & = &-15\\\Leftrightarrow & \color{red}{-25}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-15}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+12}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12-x } & = & 11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-11}& = & -13 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11+10x } & = & -13 \color{red}{ -10x }\color{blue}{+11+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &17x & = &-2\\\Leftrightarrow & \color{red}{17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+9}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9+11x } & = & -15 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &26x & = &-24\\\Leftrightarrow & \color{red}{26}x & = &-24\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-24}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+3}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-13x } & = & 8 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 8 \color{blue}{-3} \\\Leftrightarrow &-19x & = &5\\\Leftrightarrow & \color{red}{-19}x & = &5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)