Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+6}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6-x } & = & -14 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &2x & = &-20\\\Leftrightarrow & \color{red}{2}x & = &-20\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-20}{2} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+13}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13+7x } & = & -3 \color{red}{ -7x }\color{blue}{-13+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -3 \color{blue}{-13} \\\Leftrightarrow &15x & = &-16\\\Leftrightarrow & \color{red}{15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-16}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-x } & = & -3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+4}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-7x } & = & 6 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & 6 \color{blue}{-4} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-15}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-x } & = & 9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &-10x & = &24\\\Leftrightarrow & \color{red}{-10}x & = &24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-6}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{-6}\color{blue}{+6-7x } & = & -7 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -7 \color{blue}{+6} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+4}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4-x } & = & 6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 6 \color{blue}{-4} \\\Leftrightarrow &13x & = &2\\\Leftrightarrow & \color{red}{13}x & = &2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-14}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & 10 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{+14} \\\Leftrightarrow &-15x & = &24\\\Leftrightarrow & \color{red}{-15}x & = &24\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{24}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+14}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14-5x } & = & -15 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & -15 \color{blue}{-14} \\\Leftrightarrow &8x & = &-29\\\Leftrightarrow & \color{red}{8}x & = &-29\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-29}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{8} } & & \\ & V = \left\{ \frac{-29}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+14}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-7x } & = & 7 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 7 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+15}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-x } & = & -12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &-9x & = &-27\\\Leftrightarrow & \color{red}{-9}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-27}{-9} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-13}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-13}\color{blue}{+13-7x } & = & 12 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &8x & = &25\\\Leftrightarrow & \color{red}{8}x & = &25\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{25}{8} \\\Leftrightarrow & \color{green}{ x = \frac{25}{8} } & & \\ & V = \left\{ \frac{25}{8} \right\} & \\\end{align}\)