Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-14}& = & 14 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14+5x } & = & 14 \color{red}{ -5x }\color{blue}{+14+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &11x & = &28\\\Leftrightarrow & \color{red}{11}x & = &28\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{28}{11} \\\Leftrightarrow & \color{green}{ x = \frac{28}{11} } & & \\ & V = \left\{ \frac{28}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-3}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3-x } & = & -2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-12}& = & 11 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-12}\color{blue}{+12+3x } & = & 11 \color{red}{ -3x }\color{blue}{+12+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 11 \color{blue}{+12} \\\Leftrightarrow &13x & = &23\\\Leftrightarrow & \color{red}{13}x & = &23\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{23}{13} \\\Leftrightarrow & \color{green}{ x = \frac{23}{13} } & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-11}& = & -14 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11+12x } & = & -14 \color{red}{ -12x }\color{blue}{+11+12x } \\\Leftrightarrow & -x \color{blue}{+12x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6-x } & = & -3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+2}& = & -9 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-3x } & = & -9 \color{red}{ +3x }\color{blue}{-2-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -9 \color{blue}{-2} \\\Leftrightarrow &-x & = &-11\\\Leftrightarrow & \color{red}{-}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-11}{-1} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-x } & = & 13 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{-5} \\\Leftrightarrow &-10x & = &8\\\Leftrightarrow & \color{red}{-10}x & = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-9}& = & 8 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9-4x } & = & 8 \color{red}{ +4x }\color{blue}{+9-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & 8 \color{blue}{+9} \\\Leftrightarrow &7x & = &17\\\Leftrightarrow & \color{red}{7}x & = &17\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{17}{7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+14}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14-9x } & = & -5 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & -x \color{blue}{-9x } & = & -5 \color{blue}{-14} \\\Leftrightarrow &-10x & = &-19\\\Leftrightarrow & \color{red}{-10}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+4}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-13x } & = & -2 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+9}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9-x } & = & -6 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &8x & = &-15\\\Leftrightarrow & \color{red}{8}x & = &-15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+5}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & -6 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -6 \color{blue}{-5} \\\Leftrightarrow &-12x & = &-11\\\Leftrightarrow & \color{red}{-12}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-11}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{12} } & & \\ & V = \left\{ \frac{11}{12} \right\} & \\\end{align}\)