Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-12}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12-9x } & = & 2 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &-7x & = &14\\\Leftrightarrow & \color{red}{-7}x & = &14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{14}{-7} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-13}& = & 6 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-14x } & = & 6 \color{red}{ +14x }\color{blue}{+13-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 6 \color{blue}{+13} \\\Leftrightarrow &-27x & = &19\\\Leftrightarrow & \color{red}{-27}x & = &19\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{19}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{27} } & & \\ & V = \left\{ \frac{-19}{27} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13-x } & = & 11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &-13x & = &24\\\Leftrightarrow & \color{red}{-13}x & = &24\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{24}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{13} } & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+13}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-x } & = & -2 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -2 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-15\\\Leftrightarrow & \color{red}{-13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-3}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-x } & = & -5 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-x } & = & -10 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -10 \color{blue}{+1} \\\Leftrightarrow &-12x & = &-9\\\Leftrightarrow & \color{red}{-12}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-15}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-x } & = & 6 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 6 \color{blue}{+15} \\\Leftrightarrow &-7x & = &21\\\Leftrightarrow & \color{red}{-7}x & = &21\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{21}{-7} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-x } & = & -3 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+15}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-11x } & = & 6 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 6 \color{blue}{-15} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-13}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-x } & = & 3 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 3 \color{blue}{+13} \\\Leftrightarrow &-7x & = &16\\\Leftrightarrow & \color{red}{-7}x & = &16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-12}& = & 13 \color{red}{ +6x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12-6x } & = & 13 \color{red}{ +6x }\color{blue}{+12-6x } \\\Leftrightarrow & 11x \color{blue}{-6x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &5x & = &25\\\Leftrightarrow & \color{red}{5}x & = &25\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{25}{5} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-x } & = & 4 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 4 \color{blue}{+13} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)