Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+12}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+12}\color{blue}{-12-13x } & = & 9 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &-25x & = &-3\\\Leftrightarrow & \color{red}{-25}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-3}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{3}{25} } & & \\ & V = \left\{ \frac{3}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-15}& = & 5 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15+9x } & = & 5 \color{red}{ -9x }\color{blue}{+15+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 5 \color{blue}{+15} \\\Leftrightarrow &19x & = &20\\\Leftrightarrow & \color{red}{19}x & = &20\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{20}{19} \\\Leftrightarrow & \color{green}{ x = \frac{20}{19} } & & \\ & V = \left\{ \frac{20}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-6}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6-9x } & = & 4 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & 4 \color{blue}{+6} \\\Leftrightarrow &-2x & = &10\\\Leftrightarrow & \color{red}{-2}x & = &10\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{10}{-2} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+15}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15+11x } & = & -8 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &23x & = &-23\\\Leftrightarrow & \color{red}{23}x & = &-23\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-23}{23} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-12}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-12}\color{blue}{+12-13x } & = & 3 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &-3x & = &15\\\Leftrightarrow & \color{red}{-3}x & = &15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{15}{-3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+14}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14-x } & = & -3 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &13x & = &-17\\\Leftrightarrow & \color{red}{13}x & = &-17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-13}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-x } & = & 2 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 2 \color{blue}{+13} \\\Leftrightarrow &-9x & = &15\\\Leftrightarrow & \color{red}{-9}x & = &15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+6}& = & -4 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6+6x } & = & -4 \color{red}{ -6x }\color{blue}{-6+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -4 \color{blue}{-6} \\\Leftrightarrow &19x & = &-10\\\Leftrightarrow & \color{red}{19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+1}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-13x } & = & -9 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &-25x & = &-10\\\Leftrightarrow & \color{red}{-25}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-10}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+15}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15+11x } & = & 8 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &17x & = &-7\\\Leftrightarrow & \color{red}{17}x & = &-7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+2}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2-5x } & = & 2 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & 9x \color{blue}{-5x } & = & 2 \color{blue}{-2} \\\Leftrightarrow &4x & = &0\\\Leftrightarrow & \color{red}{4}x & = &0\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{0}{4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-11}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-13x } & = & 13 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &-19x & = &24\\\Leftrightarrow & \color{red}{-19}x & = &24\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{24}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{19} } & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)