Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-12}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-12}\color{blue}{+12-5x } & = & 2 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &-9x & = &14\\\Leftrightarrow & \color{red}{-9}x & = &14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-14}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14+11x } & = & 11 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & 11 \color{blue}{+14} \\\Leftrightarrow &14x & = &25\\\Leftrightarrow & \color{red}{14}x & = &25\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{25}{14} \\\Leftrightarrow & \color{green}{ x = \frac{25}{14} } & & \\ & V = \left\{ \frac{25}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & 2 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-9}& = & -1 \color{red}{ -5x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9+5x } & = & -1 \color{red}{ -5x }\color{blue}{+9+5x } \\\Leftrightarrow & -x \color{blue}{+5x } & = & -1 \color{blue}{+9} \\\Leftrightarrow &4x & = &8\\\Leftrightarrow & \color{red}{4}x & = &8\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{8}{4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-8}& = & 13 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8+6x } & = & 13 \color{red}{ -6x }\color{blue}{+8+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 13 \color{blue}{+8} \\\Leftrightarrow &13x & = &21\\\Leftrightarrow & \color{red}{13}x & = &21\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{21}{13} \\\Leftrightarrow & \color{green}{ x = \frac{21}{13} } & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+5}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-3x } & = & -11 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &-5x & = &-16\\\Leftrightarrow & \color{red}{-5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+5}& = & 14 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5-10x } & = & 14 \color{red}{ +10x }\color{blue}{-5-10x } \\\Leftrightarrow & 11x \color{blue}{-10x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+13}& = & -14 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13+9x } & = & -14 \color{red}{ -9x }\color{blue}{-13+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -14 \color{blue}{-13} \\\Leftrightarrow &19x & = &-27\\\Leftrightarrow & \color{red}{19}x & = &-27\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-27}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{19} } & & \\ & V = \left\{ \frac{-27}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-x } & = & 14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+6}& = & 11 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6+4x } & = & 11 \color{red}{ -4x }\color{blue}{-6+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 11 \color{blue}{-6} \\\Leftrightarrow &9x & = &5\\\Leftrightarrow & \color{red}{9}x & = &5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+14}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14+11x } & = & 15 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 15 \color{blue}{-14} \\\Leftrightarrow &23x & = &1\\\Leftrightarrow & \color{red}{23}x & = &1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{1}{23} } & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-12}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12-x } & = & -14 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)