Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+3}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3-7x } & = & 1 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & 1 \color{blue}{-3} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+6}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6-7x } & = & -3 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &2x & = &-9\\\Leftrightarrow & \color{red}{2}x & = &-9\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-9}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-12}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-13x } & = & 11 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 11 \color{blue}{+12} \\\Leftrightarrow &-25x & = &23\\\Leftrightarrow & \color{red}{-25}x & = &23\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{23}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{25} } & & \\ & V = \left\{ \frac{-23}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+2}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-x } & = & -13 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -13 \color{blue}{-2} \\\Leftrightarrow &-9x & = &-15\\\Leftrightarrow & \color{red}{-9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-14}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x } & = & -1 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &-9x & = &13\\\Leftrightarrow & \color{red}{-9}x & = &13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-12}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12-11x } & = & 15 \color{red}{ +11x }\color{blue}{+12-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 15 \color{blue}{+12} \\\Leftrightarrow &-5x & = &27\\\Leftrightarrow & \color{red}{-5}x & = &27\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{27}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{5} } & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-5}& = & 15 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5+6x } & = & 15 \color{red}{ -6x }\color{blue}{+5+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 15 \color{blue}{+5} \\\Leftrightarrow &19x & = &20\\\Leftrightarrow & \color{red}{19}x & = &20\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{20}{19} \\\Leftrightarrow & \color{green}{ x = \frac{20}{19} } & & \\ & V = \left\{ \frac{20}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-14}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14-x } & = & 13 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 13 \color{blue}{+14} \\\Leftrightarrow &-16x & = &27\\\Leftrightarrow & \color{red}{-16}x & = &27\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{27}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{16} } & & \\ & V = \left\{ \frac{-27}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+3}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3-x } & = & -9 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & -9 \color{blue}{-3} \\\Leftrightarrow &14x & = &-12\\\Leftrightarrow & \color{red}{14}x & = &-12\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-12}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11-x } & = & 13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &-3x & = &24\\\Leftrightarrow & \color{red}{-3}x & = &24\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{24}{-3} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-14}& = & 10 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14+9x } & = & 10 \color{red}{ -9x }\color{blue}{+14+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 10 \color{blue}{+14} \\\Leftrightarrow &14x & = &24\\\Leftrightarrow & \color{red}{14}x & = &24\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{24}{14} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-1}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-3x } & = & 4 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & 4 \color{blue}{+1} \\\Leftrightarrow &-14x & = &5\\\Leftrightarrow & \color{red}{-14}x & = &5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)