Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-14}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14-x } & = & -5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -5 \color{blue}{+14} \\\Leftrightarrow &-13x & = &9\\\Leftrightarrow & \color{red}{-13}x & = &9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-15}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-x } & = & -10 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+15}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-x } & = & -13 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &-8x & = &-28\\\Leftrightarrow & \color{red}{-8}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-28}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+14}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-13x } & = & 3 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &-25x & = &-11\\\Leftrightarrow & \color{red}{-25}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-11}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{11}{25} } & & \\ & V = \left\{ \frac{11}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+12}& = & -11 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12+6x } & = & -11 \color{red}{ -6x }\color{blue}{-12+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -11 \color{blue}{-12} \\\Leftrightarrow &13x & = &-23\\\Leftrightarrow & \color{red}{13}x & = &-23\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-23}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{13} } & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13-x } & = & -1 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &-14x & = &-14\\\Leftrightarrow & \color{red}{-14}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-14}{-14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-8}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-7x } & = & -4 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &-16x & = &4\\\Leftrightarrow & \color{red}{-16}x & = &4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+10}& = & -1 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10+4x } & = & -1 \color{red}{ -4x }\color{blue}{-10+4x } \\\Leftrightarrow & x \color{blue}{+4x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &5x & = &-11\\\Leftrightarrow & \color{red}{5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-10}& = & -3 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10+9x } & = & -3 \color{red}{ -9x }\color{blue}{+10+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & -3 \color{blue}{+10} \\\Leftrightarrow &16x & = &7\\\Leftrightarrow & \color{red}{16}x & = &7\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{7}{16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-x } & = & -8 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -8 \color{blue}{+15} \\\Leftrightarrow &-5x & = &7\\\Leftrightarrow & \color{red}{-5}x & = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-14}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14-x } & = & 10 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 10 \color{blue}{+14} \\\Leftrightarrow &-7x & = &24\\\Leftrightarrow & \color{red}{-7}x & = &24\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{24}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{7} } & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+13}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-13x } & = & 1 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 1 \color{blue}{-13} \\\Leftrightarrow &-25x & = &-12\\\Leftrightarrow & \color{red}{-25}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-12}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{12}{25} } & & \\ & V = \left\{ \frac{12}{25} \right\} & \\\end{align}\)