Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-11}& = & -14 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11-12x } & = & -14 \color{red}{ +12x }\color{blue}{+11-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+12}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-x } & = & 2 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &-16x & = &-10\\\Leftrightarrow & \color{red}{-16}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11-x } & = & -8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &10x & = &-19\\\Leftrightarrow & \color{red}{10}x & = &-19\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-19}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{10} } & & \\ & V = \left\{ \frac{-19}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+7}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7-13x } & = & 6 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+11}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-7x } & = & 4 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & 4 \color{blue}{-11} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-5}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{-5}\color{blue}{+5-5x } & = & -11 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & -11 \color{blue}{+5} \\\Leftrightarrow &9x & = &-6\\\Leftrightarrow & \color{red}{9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-12}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12-13x } & = & -12 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & -12 \color{blue}{+12} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-15}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-x } & = & 1 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 1 \color{blue}{+15} \\\Leftrightarrow &-3x & = &16\\\Leftrightarrow & \color{red}{-3}x & = &16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-x } & = & 14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &-16x & = &21\\\Leftrightarrow & \color{red}{-16}x & = &21\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{21}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{16} } & & \\ & V = \left\{ \frac{-21}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+13}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13-x } & = & -13 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -13 \color{blue}{-13} \\\Leftrightarrow &13x & = &-26\\\Leftrightarrow & \color{red}{13}x & = &-26\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-26}{13} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-14}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14-11x } & = & 4 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 4 \color{blue}{+14} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-9}& = & -7 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-9}\color{blue}{+9-8x } & = & -7 \color{red}{ +8x }\color{blue}{+9-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -7 \color{blue}{+9} \\\Leftrightarrow &-15x & = &2\\\Leftrightarrow & \color{red}{-15}x & = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)