Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+13}& = & -15 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13+8x } & = & -15 \color{red}{ -8x }\color{blue}{-13+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &19x & = &-28\\\Leftrightarrow & \color{red}{19}x & = &-28\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-28}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{19} } & & \\ & V = \left\{ \frac{-28}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+12}& = & -14 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-6x } & = & -14 \color{red}{ +6x }\color{blue}{-12-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -14 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-26\\\Leftrightarrow & \color{red}{-11}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-26}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{26}{11} } & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-5}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-9x } & = & 4 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-7}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7-9x } & = & -5 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & 5x \color{blue}{-9x } & = & -5 \color{blue}{+7} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-5}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5+11x } & = & 11 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &17x & = &16\\\Leftrightarrow & \color{red}{17}x & = &16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+11}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11-x } & = & 5 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 5 \color{blue}{-11} \\\Leftrightarrow &5x & = &-6\\\Leftrightarrow & \color{red}{5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-5}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-x } & = & -5 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-6}& = & 13 \color{red}{ -2x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6+2x } & = & 13 \color{red}{ -2x }\color{blue}{+6+2x } \\\Leftrightarrow & 13x \color{blue}{+2x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &15x & = &19\\\Leftrightarrow & \color{red}{15}x & = &19\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{19}{15} \\\Leftrightarrow & \color{green}{ x = \frac{19}{15} } & & \\ & V = \left\{ \frac{19}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+4}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4-13x } & = & -15 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &-18x & = &-19\\\Leftrightarrow & \color{red}{-18}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-19}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{19}{18} } & & \\ & V = \left\{ \frac{19}{18} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-6}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-6}\color{blue}{+6-x } & = & 1 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &-3x & = &7\\\Leftrightarrow & \color{red}{-3}x & = &7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-x } & = & 7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)