Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-6}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6-5x } & = & -5 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &9x & = &1\\\Leftrightarrow & \color{red}{9}x & = &1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+6}& = & -1 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6+13x } & = & -1 \color{red}{ -13x }\color{blue}{-6+13x } \\\Leftrightarrow & x \color{blue}{+13x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &14x & = &-7\\\Leftrightarrow & \color{red}{14}x & = &-7\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-7}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+13}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13-7x } & = & -3 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & -3 \color{blue}{-13} \\\Leftrightarrow &-x & = &-16\\\Leftrightarrow & \color{red}{-}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-16}{-1} \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+4}& = & 5 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4+9x } & = & 5 \color{red}{ -9x }\color{blue}{-4+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &23x & = &1\\\Leftrightarrow & \color{red}{23}x & = &1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{1}{23} } & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-12}& = & -3 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12+5x } & = & -3 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -3 \color{blue}{+12} \\\Leftrightarrow &16x & = &9\\\Leftrightarrow & \color{red}{16}x & = &9\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{9}{16} \\\Leftrightarrow & \color{green}{ x = \frac{9}{16} } & & \\ & V = \left\{ \frac{9}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-1}& = & -8 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1+8x } & = & -8 \color{red}{ -8x }\color{blue}{+1+8x } \\\Leftrightarrow & x \color{blue}{+8x } & = & -8 \color{blue}{+1} \\\Leftrightarrow &9x & = &-7\\\Leftrightarrow & \color{red}{9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-7}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-14}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-11x } & = & -1 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & -13x \color{blue}{-11x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &-24x & = &13\\\Leftrightarrow & \color{red}{-24}x & = &13\\\Leftrightarrow & \frac{\color{red}{-24}x}{ \color{blue}{ -24}} & = & \frac{13}{-24} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{24} } & & \\ & V = \left\{ \frac{-13}{24} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-15}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-x } & = & -4 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -4 \color{blue}{+15} \\\Leftrightarrow &-16x & = &11\\\Leftrightarrow & \color{red}{-16}x & = &11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{16} } & & \\ & V = \left\{ \frac{-11}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-4}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-4}\color{blue}{+4-7x } & = & 13 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 13 \color{blue}{+4} \\\Leftrightarrow &-20x & = &17\\\Leftrightarrow & \color{red}{-20}x & = &17\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{17}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{20} } & & \\ & V = \left\{ \frac{-17}{20} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-14}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-x } & = & 8 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 8 \color{blue}{+14} \\\Leftrightarrow &-14x & = &22\\\Leftrightarrow & \color{red}{-14}x & = &22\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{22}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-13}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-x } & = & -8 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-10}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10-13x } & = & -7 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)