Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+1}& = & -12 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1+5x } & = & -12 \color{red}{ -5x }\color{blue}{-1+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &11x & = &-13\\\Leftrightarrow & \color{red}{11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-13}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-x } & = & 3 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-3}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3-3x } & = & 10 \color{red}{ +3x }\color{blue}{+3-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &7x & = &13\\\Leftrightarrow & \color{red}{7}x & = &13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+6}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6-11x } & = & 5 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-13}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-9x } & = & 4 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 4 \color{blue}{+13} \\\Leftrightarrow &-20x & = &17\\\Leftrightarrow & \color{red}{-20}x & = &17\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{17}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{20} } & & \\ & V = \left\{ \frac{-17}{20} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-x } & = & -14 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-1}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1-x } & = & -1 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -1 \color{blue}{+1} \\\Leftrightarrow &13x & = &0\\\Leftrightarrow & \color{red}{13}x & = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+4}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-x } & = & 2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-14}& = & -13 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14+5x } & = & -13 \color{red}{ -5x }\color{blue}{+14+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &16x & = &1\\\Leftrightarrow & \color{red}{16}x & = &1\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{1}{16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+2}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2-13x } & = & -13 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -13 \color{blue}{-2} \\\Leftrightarrow &-28x & = &-15\\\Leftrightarrow & \color{red}{-28}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-15}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{15}{28} } & & \\ & V = \left\{ \frac{15}{28} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-13}& = & -3 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13-12x } & = & -3 \color{red}{ +12x }\color{blue}{+13-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -3 \color{blue}{+13} \\\Leftrightarrow &-x & = &10\\\Leftrightarrow & \color{red}{-}x & = &10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{10}{-1} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+6}& = & -1 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6+7x } & = & -1 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &11x & = &-7\\\Leftrightarrow & \color{red}{11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)