Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-9}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-13x } & = & -10 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-4}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-9x } & = & 12 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &-7x & = &16\\\Leftrightarrow & \color{red}{-7}x & = &16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-1}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-9x } & = & -14 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -14 \color{blue}{+1} \\\Leftrightarrow &-17x & = &-13\\\Leftrightarrow & \color{red}{-17}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-13}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+3}& = & 12 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3+10x } & = & 12 \color{red}{ -10x }\color{blue}{-3+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &21x & = &9\\\Leftrightarrow & \color{red}{21}x & = &9\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{9}{21} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-12}& = & -2 \color{red}{ -14x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12+14x } & = & -2 \color{red}{ -14x }\color{blue}{+12+14x } \\\Leftrightarrow & -x \color{blue}{+14x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &13x & = &10\\\Leftrightarrow & \color{red}{13}x & = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+14}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14+11x } & = & 9 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &17x & = &-5\\\Leftrightarrow & \color{red}{17}x & = &-5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{17} } & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-8}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-9x } & = & -8 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -8 \color{blue}{+8} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+11}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11-x } & = & 15 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &10x & = &4\\\Leftrightarrow & \color{red}{10}x & = &4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-9}& = & 10 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9+2x } & = & 10 \color{red}{ -2x }\color{blue}{+9+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &17x & = &19\\\Leftrightarrow & \color{red}{17}x & = &19\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{19}{17} \\\Leftrightarrow & \color{green}{ x = \frac{19}{17} } & & \\ & V = \left\{ \frac{19}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-5}& = & -5 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5+15x } & = & -5 \color{red}{ -15x }\color{blue}{+5+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &23x & = &0\\\Leftrightarrow & \color{red}{23}x & = &0\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{0}{23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+5}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-x } & = & -10 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -10 \color{blue}{-5} \\\Leftrightarrow &-3x & = &-15\\\Leftrightarrow & \color{red}{-3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-15}{-3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-1}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-x } & = & 13 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &-9x & = &14\\\Leftrightarrow & \color{red}{-9}x & = &14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)