Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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