Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-1}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1-5x } & = & -5 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -5 \color{blue}{+1} \\\Leftrightarrow &x & = &-4\\\Leftrightarrow & \color{red}{}x & = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-x } & = & 6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-12x & = &5\\\Leftrightarrow & \color{red}{-12}x & = &5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-12}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-5x } & = & -14 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &-17x & = &-2\\\Leftrightarrow & \color{red}{-17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+5}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5-11x } & = & -14 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -14 \color{blue}{-5} \\\Leftrightarrow &-5x & = &-19\\\Leftrightarrow & \color{red}{-5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-x } & = & -1 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -1 \color{blue}{+13} \\\Leftrightarrow &-4x & = &12\\\Leftrightarrow & \color{red}{-4}x & = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-7}& = & 7 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7+6x } & = & 7 \color{red}{ -6x }\color{blue}{+7+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 7 \color{blue}{+7} \\\Leftrightarrow &19x & = &14\\\Leftrightarrow & \color{red}{19}x & = &14\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{14}{19} \\\Leftrightarrow & \color{green}{ x = \frac{14}{19} } & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-13}& = & -10 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13+6x } & = & -10 \color{red}{ -6x }\color{blue}{+13+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -10 \color{blue}{+13} \\\Leftrightarrow &19x & = &3\\\Leftrightarrow & \color{red}{19}x & = &3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-6}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6-5x } & = & 3 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & 7x \color{blue}{-5x } & = & 3 \color{blue}{+6} \\\Leftrightarrow &2x & = &9\\\Leftrightarrow & \color{red}{2}x & = &9\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{9}{2} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-5}& = & 9 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5+5x } & = & 9 \color{red}{ -5x }\color{blue}{+5+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 9 \color{blue}{+5} \\\Leftrightarrow &13x & = &14\\\Leftrightarrow & \color{red}{13}x & = &14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+5}& = & 13 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-6x } & = & 13 \color{red}{ +6x }\color{blue}{-5-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 13 \color{blue}{-5} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+10}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-x } & = & -12 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -12 \color{blue}{-10} \\\Leftrightarrow &-4x & = &-22\\\Leftrightarrow & \color{red}{-4}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-22}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-x } & = & 7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &-9x & = &20\\\Leftrightarrow & \color{red}{-9}x & = &20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{9} } & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)