Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-12}& = & -6 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12+2x } & = & -6 \color{red}{ -2x }\color{blue}{+12+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -6 \color{blue}{+12} \\\Leftrightarrow &17x & = &6\\\Leftrightarrow & \color{red}{17}x & = &6\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{6}{17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{-10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10-x } & = & 13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &12x & = &23\\\Leftrightarrow & \color{red}{12}x & = &23\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{23}{12} \\\Leftrightarrow & \color{green}{ x = \frac{23}{12} } & & \\ & V = \left\{ \frac{23}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-1}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1-x } & = & -1 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -1 \color{blue}{+1} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-x } & = & -14 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -14 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-27\\\Leftrightarrow & \color{red}{-13}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-27}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{27}{13} } & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-4}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-4}\color{blue}{+4-x } & = & 10 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{+4} \\\Leftrightarrow &-15x & = &14\\\Leftrightarrow & \color{red}{-15}x & = &14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+12}& = & 2 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12+8x } & = & 2 \color{red}{ -8x }\color{blue}{-12+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &17x & = &-10\\\Leftrightarrow & \color{red}{17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+12}& = & 8 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12+4x } & = & 8 \color{red}{ -4x }\color{blue}{-12+4x } \\\Leftrightarrow & 13x \color{blue}{+4x } & = & 8 \color{blue}{-12} \\\Leftrightarrow &17x & = &-4\\\Leftrightarrow & \color{red}{17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-8}& = & -9 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8-2x } & = & -9 \color{red}{ +2x }\color{blue}{+8-2x } \\\Leftrightarrow & 13x \color{blue}{-2x } & = & -9 \color{blue}{+8} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+8}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8-x } & = & -4 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -4 \color{blue}{-8} \\\Leftrightarrow &-16x & = &-12\\\Leftrightarrow & \color{red}{-16}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+5}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & 14 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+5}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-x } & = & -15 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &-3x & = &-20\\\Leftrightarrow & \color{red}{-3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-5}& = & -4 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5+12x } & = & -4 \color{red}{ -12x }\color{blue}{+5+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -4 \color{blue}{+5} \\\Leftrightarrow &25x & = &1\\\Leftrightarrow & \color{red}{25}x & = &1\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{1}{25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{25} } & & \\ & V = \left\{ \frac{1}{25} \right\} & \\\end{align}\)