Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-13}& = & 12 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-13}\color{blue}{+13+6x } & = & 12 \color{red}{ -6x }\color{blue}{+13+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &13x & = &25\\\Leftrightarrow & \color{red}{13}x & = &25\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{25}{13} \\\Leftrightarrow & \color{green}{ x = \frac{25}{13} } & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-13}& = & 2 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13+8x } & = & 2 \color{red}{ -8x }\color{blue}{+13+8x } \\\Leftrightarrow & -x \color{blue}{+8x } & = & 2 \color{blue}{+13} \\\Leftrightarrow &7x & = &15\\\Leftrightarrow & \color{red}{7}x & = &15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{15}{7} } & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-2}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2-13x } & = & 8 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &-16x & = &10\\\Leftrightarrow & \color{red}{-16}x & = &10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-5}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-x } & = & 6 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 6 \color{blue}{+5} \\\Leftrightarrow &-7x & = &11\\\Leftrightarrow & \color{red}{-7}x & = &11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-1}& = & 6 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1+7x } & = & 6 \color{red}{ -7x }\color{blue}{+1+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & 6 \color{blue}{+1} \\\Leftrightarrow &12x & = &7\\\Leftrightarrow & \color{red}{12}x & = &7\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{7}{12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-11}& = & 9 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-10x } & = & 9 \color{red}{ +10x }\color{blue}{+11-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &-13x & = &20\\\Leftrightarrow & \color{red}{-13}x & = &20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{13} } & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-6}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-13x } & = & -6 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &-17x & = &0\\\Leftrightarrow & \color{red}{-17}x & = &0\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{0}{-17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-11}& = & -4 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11-8x } & = & -4 \color{red}{ +8x }\color{blue}{+11-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &-15x & = &7\\\Leftrightarrow & \color{red}{-15}x & = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+4}& = & -15 \color{red}{ -6x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4+6x } & = & -15 \color{red}{ -6x }\color{blue}{-4+6x } \\\Leftrightarrow & -x \color{blue}{+6x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &5x & = &-19\\\Leftrightarrow & \color{red}{5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-19}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+15}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-9x } & = & 15 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 15 \color{blue}{-15} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-1}& = & -4 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1+11x } & = & -4 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -4 \color{blue}{+1} \\\Leftrightarrow &25x & = &-3\\\Leftrightarrow & \color{red}{25}x & = &-3\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-3}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{25} } & & \\ & V = \left\{ \frac{-3}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+12}& = & -4 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12+9x } & = & -4 \color{red}{ -9x }\color{blue}{-12+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -4 \color{blue}{-12} \\\Leftrightarrow &14x & = &-16\\\Leftrightarrow & \color{red}{14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-16}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)