Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+13}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13+5x } & = & 2 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 2 \color{blue}{-13} \\\Leftrightarrow &16x & = &-11\\\Leftrightarrow & \color{red}{16}x & = &-11\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-11}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{16} } & & \\ & V = \left\{ \frac{-11}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & -14 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -14 \color{blue}{-2} \\\Leftrightarrow &-4x & = &-16\\\Leftrightarrow & \color{red}{-4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-16}{-4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-2}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2-13x } & = & -9 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & -9 \color{blue}{+2} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+13}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-x } & = & 8 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 8 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-5\\\Leftrightarrow & \color{red}{-13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+15}& = & -4 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15+5x } & = & -4 \color{red}{ -5x }\color{blue}{-15+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -4 \color{blue}{-15} \\\Leftrightarrow &11x & = &-19\\\Leftrightarrow & \color{red}{11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-19}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{11} } & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-7}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-x } & = & -2 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-3}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3-4x } & = & -7 \color{red}{ +4x }\color{blue}{+3-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -7 \color{blue}{+3} \\\Leftrightarrow &5x & = &-4\\\Leftrightarrow & \color{red}{5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+15}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-x } & = & -15 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -15 \color{blue}{-15} \\\Leftrightarrow &-10x & = &-30\\\Leftrightarrow & \color{red}{-10}x & = &-30\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-30}{-10} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-12}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-5x } & = & -9 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -9 \color{blue}{+12} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-4}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-4}\color{blue}{+4-x } & = & -5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+13}& = & 8 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13-4x } & = & 8 \color{red}{ +4x }\color{blue}{-13-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & 8 \color{blue}{-13} \\\Leftrightarrow &5x & = &-5\\\Leftrightarrow & \color{red}{5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-15}& = & -15 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15-10x } & = & -15 \color{red}{ +10x }\color{blue}{+15-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & -15 \color{blue}{+15} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)