Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-6}& = & -11 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6-14x } & = & -11 \color{red}{ +14x }\color{blue}{+6-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -11 \color{blue}{+6} \\\Leftrightarrow &-23x & = &-5\\\Leftrightarrow & \color{red}{-23}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-5}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{5}{23} } & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-13}& = & -14 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13+x } & = & -14 \color{red}{ -x }\color{blue}{+13+x } \\\Leftrightarrow & x \color{blue}{+x } & = & -14 \color{blue}{+13} \\\Leftrightarrow &2x & = &-1\\\Leftrightarrow & \color{red}{2}x & = &-1\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-1}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+9}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9-13x } & = & 6 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & 6 \color{blue}{-9} \\\Leftrightarrow &2x & = &-3\\\Leftrightarrow & \color{red}{2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-4}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-13x } & = & -3 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &-25x & = &1\\\Leftrightarrow & \color{red}{-25}x & = &1\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{1}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{25} } & & \\ & V = \left\{ \frac{-1}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-x } & = & 1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+5}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5-13x } & = & -14 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -14 \color{blue}{-5} \\\Leftrightarrow &-3x & = &-19\\\Leftrightarrow & \color{red}{-3}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-19}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{19}{3} } & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-5}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5+11x } & = & 1 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 1 \color{blue}{+5} \\\Leftrightarrow &26x & = &6\\\Leftrightarrow & \color{red}{26}x & = &6\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{6}{26} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+6}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-13x } & = & -5 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &-18x & = &-11\\\Leftrightarrow & \color{red}{-18}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-11}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{11}{18} } & & \\ & V = \left\{ \frac{11}{18} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-3}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-7x } & = & -13 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -13 \color{blue}{+3} \\\Leftrightarrow &-20x & = &-10\\\Leftrightarrow & \color{red}{-20}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-10}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-6}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{-6}\color{blue}{+6-9x } & = & 12 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &-11x & = &18\\\Leftrightarrow & \color{red}{-11}x & = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+4}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+4}\color{blue}{-4-x } & = & 13 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &-4x & = &9\\\Leftrightarrow & \color{red}{-4}x & = &9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-10}& = & 11 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10+10x } & = & 11 \color{red}{ -10x }\color{blue}{+10+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &17x & = &21\\\Leftrightarrow & \color{red}{17}x & = &21\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{21}{17} \\\Leftrightarrow & \color{green}{ x = \frac{21}{17} } & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)