Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+9}& = & -2 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9+9x } & = & -2 \color{red}{ -9x }\color{blue}{-9+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &23x & = &-11\\\Leftrightarrow & \color{red}{23}x & = &-11\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-11}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{23} } & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+6}& = & 5 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6+14x } & = & 5 \color{red}{ -14x }\color{blue}{-6+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &29x & = &-1\\\Leftrightarrow & \color{red}{29}x & = &-1\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-1}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{29} } & & \\ & V = \left\{ \frac{-1}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+11}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-x } & = & 15 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-3}& = & -1 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3+14x } & = & -1 \color{red}{ -14x }\color{blue}{+3+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -1 \color{blue}{+3} \\\Leftrightarrow &19x & = &2\\\Leftrightarrow & \color{red}{19}x & = &2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{2}{19} } & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-6}& = & -6 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6+13x } & = & -6 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &20x & = &0\\\Leftrightarrow & \color{red}{20}x & = &0\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{0}{20} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-10}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10-13x } & = & -10 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -10 \color{blue}{+10} \\\Leftrightarrow &-19x & = &0\\\Leftrightarrow & \color{red}{-19}x & = &0\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{0}{-19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-10}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-x } & = & 9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 9 \color{blue}{+10} \\\Leftrightarrow &-13x & = &19\\\Leftrightarrow & \color{red}{-13}x & = &19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-10}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-13x } & = & -5 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -5 \color{blue}{+10} \\\Leftrightarrow &-25x & = &5\\\Leftrightarrow & \color{red}{-25}x & = &5\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{5}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+13}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13-x } & = & -13 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -13 \color{blue}{-13} \\\Leftrightarrow &7x & = &-26\\\Leftrightarrow & \color{red}{7}x & = &-26\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-26}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{7} } & & \\ & V = \left\{ \frac{-26}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-12}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12-7x } & = & 11 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 11 \color{blue}{+12} \\\Leftrightarrow &-17x & = &23\\\Leftrightarrow & \color{red}{-17}x & = &23\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{23}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{17} } & & \\ & V = \left\{ \frac{-23}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+4}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+4}\color{blue}{-4-x } & = & -10 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &-4x & = &-14\\\Leftrightarrow & \color{red}{-4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-14}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-15}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-x } & = & -4 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -4 \color{blue}{+15} \\\Leftrightarrow &-5x & = &11\\\Leftrightarrow & \color{red}{-5}x & = &11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)