Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-9}& = & 10 \color{red}{ +15x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9-15x } & = & 10 \color{red}{ +15x }\color{blue}{+9-15x } \\\Leftrightarrow & x \color{blue}{-15x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &-14x & = &19\\\Leftrightarrow & \color{red}{-14}x & = &19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{14} } & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-x } & = & -11 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -11 \color{blue}{-3} \\\Leftrightarrow &-14x & = &-14\\\Leftrightarrow & \color{red}{-14}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-14}{-14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+14}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14-11x } & = & 12 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-2\\\Leftrightarrow & \color{red}{-5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+12}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-13x } & = & 15 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &-17x & = &3\\\Leftrightarrow & \color{red}{-17}x & = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-4}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4-x } & = & 10 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 10 \color{blue}{+4} \\\Leftrightarrow &13x & = &14\\\Leftrightarrow & \color{red}{13}x & = &14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-8}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8-x } & = & -9 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -9 \color{blue}{+8} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5-x } & = & -9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-9x & = &-14\\\Leftrightarrow & \color{red}{-9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+6}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-x } & = & -8 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -8 \color{blue}{-6} \\\Leftrightarrow &-13x & = &-14\\\Leftrightarrow & \color{red}{-13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-x } & = & 12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &-14x & = &24\\\Leftrightarrow & \color{red}{-14}x & = &24\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{24}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+11}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11-7x } & = & 7 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -x \color{blue}{-7x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &-8x & = &-4\\\Leftrightarrow & \color{red}{-8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+7}& = & 11 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7+6x } & = & 11 \color{red}{ -6x }\color{blue}{-7+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &19x & = &4\\\Leftrightarrow & \color{red}{19}x & = &4\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{4}{19} \\\Leftrightarrow & \color{green}{ x = \frac{4}{19} } & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3-x } & = & 3 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)