Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-9}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{-9}\color{blue}{+9-14x } & = & 12 \color{red}{ +14x }\color{blue}{+9-14x } \\\Leftrightarrow & 3x \color{blue}{-14x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &-11x & = &21\\\Leftrightarrow & \color{red}{-11}x & = &21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+1}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-x } & = & -9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &-7x & = &-10\\\Leftrightarrow & \color{red}{-7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-13}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x } & = & 3 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 3 \color{blue}{+13} \\\Leftrightarrow &-8x & = &16\\\Leftrightarrow & \color{red}{-8}x & = &16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{16}{-8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+11}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11-x } & = & -12 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -12 \color{blue}{-11} \\\Leftrightarrow &-12x & = &-23\\\Leftrightarrow & \color{red}{-12}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-23}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{23}{12} } & & \\ & V = \left\{ \frac{23}{12} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+4}& = & -14 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4+10x } & = & -14 \color{red}{ -10x }\color{blue}{-4+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &21x & = &-18\\\Leftrightarrow & \color{red}{21}x & = &-18\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-18}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-6}& = & 14 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6+6x } & = & 14 \color{red}{ -6x }\color{blue}{+6+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 14 \color{blue}{+6} \\\Leftrightarrow &13x & = &20\\\Leftrightarrow & \color{red}{13}x & = &20\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{20}{13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+8}& = & 1 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8+6x } & = & 1 \color{red}{ -6x }\color{blue}{-8+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &19x & = &-7\\\Leftrightarrow & \color{red}{19}x & = &-7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{19} } & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+10}& = & -9 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10+14x } & = & -9 \color{red}{ -14x }\color{blue}{-10+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &17x & = &-19\\\Leftrightarrow & \color{red}{17}x & = &-19\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-19}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{17} } & & \\ & V = \left\{ \frac{-19}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-12}& = & 9 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-8x } & = & 9 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &-x & = &21\\\Leftrightarrow & \color{red}{-}x & = &21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{21}{-1} \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+8}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8-x } & = & -1 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &11x & = &-9\\\Leftrightarrow & \color{red}{11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-4}& = & -7 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-4}\color{blue}{+4-10x } & = & -7 \color{red}{ +10x }\color{blue}{+4-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -7 \color{blue}{+4} \\\Leftrightarrow &-19x & = &-3\\\Leftrightarrow & \color{red}{-19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+14}& = & -15 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14+13x } & = & -15 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -15 \color{blue}{-14} \\\Leftrightarrow &23x & = &-29\\\Leftrightarrow & \color{red}{23}x & = &-29\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-29}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{23} } & & \\ & V = \left\{ \frac{-29}{23} \right\} & \\\end{align}\)