Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-x } & = & 13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &-4x & = &24\\\Leftrightarrow & \color{red}{-4}x & = &24\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{24}{-4} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-12}& = & 6 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12-3x } & = & 6 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & 6 \color{blue}{+12} \\\Leftrightarrow &-14x & = &18\\\Leftrightarrow & \color{red}{-14}x & = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-5}& = & -9 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5-14x } & = & -9 \color{red}{ +14x }\color{blue}{+5-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &-27x & = &-4\\\Leftrightarrow & \color{red}{-27}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-4}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{4}{27} } & & \\ & V = \left\{ \frac{4}{27} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+15}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15-x } & = & 10 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 10 \color{blue}{-15} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-3}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3-7x } & = & 5 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 5 \color{blue}{+3} \\\Leftrightarrow &x & = &8\\\Leftrightarrow & \color{red}{}x & = &8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 8 \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-11}& = & 3 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11-2x } & = & 3 \color{red}{ +2x }\color{blue}{+11-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &7x & = &14\\\Leftrightarrow & \color{red}{7}x & = &14\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{14}{7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+7}& = & -11 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7+5x } & = & -11 \color{red}{ -5x }\color{blue}{-7+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &11x & = &-18\\\Leftrightarrow & \color{red}{11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-5}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5-x } & = & 14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &-14x & = &19\\\Leftrightarrow & \color{red}{-14}x & = &19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{14} } & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-14}& = & -5 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14+11x } & = & -5 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -5 \color{blue}{+14} \\\Leftrightarrow &17x & = &9\\\Leftrightarrow & \color{red}{17}x & = &9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+7}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7-13x } & = & 9 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+12}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+12}\color{blue}{-12-x } & = & -15 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &13x & = &-27\\\Leftrightarrow & \color{red}{13}x & = &-27\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-27}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{13} } & & \\ & V = \left\{ \frac{-27}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+14}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-x } & = & -10 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -10 \color{blue}{-14} \\\Leftrightarrow &-3x & = &-24\\\Leftrightarrow & \color{red}{-3}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-24}{-3} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)