Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+12}& = & -10 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12+5x } & = & -10 \color{red}{ -5x }\color{blue}{-12+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &8x & = &-22\\\Leftrightarrow & \color{red}{8}x & = &-22\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-22}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-2}& = & 2 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-2}\color{blue}{+2+15x } & = & 2 \color{red}{ -15x }\color{blue}{+2+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & 2 \color{blue}{+2} \\\Leftrightarrow &14x & = &4\\\Leftrightarrow & \color{red}{14}x & = &4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-13}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13-x } & = & -9 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -9 \color{blue}{+13} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-13}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13-x } & = & -13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -13 \color{blue}{+13} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-3}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-x } & = & -8 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-15}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{-15}\color{blue}{+15+5x } & = & 2 \color{red}{ -5x }\color{blue}{+15+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & 2 \color{blue}{+15} \\\Leftrightarrow &6x & = &17\\\Leftrightarrow & \color{red}{6}x & = &17\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{17}{6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+4}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4-11x } & = & 11 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 11 \color{blue}{-4} \\\Leftrightarrow &4x & = &7\\\Leftrightarrow & \color{red}{4}x & = &7\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{7}{4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+5}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-x } & = & 15 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &-10x & = &10\\\Leftrightarrow & \color{red}{-10}x & = &10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{10}{-10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+13}& = & 13 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13-12x } & = & 13 \color{red}{ +12x }\color{blue}{-13-12x } \\\Leftrightarrow & 5x \color{blue}{-12x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-14}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14-13x } & = & -12 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -12 \color{blue}{+14} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-1}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-x } & = & -5 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -5 \color{blue}{+1} \\\Leftrightarrow &-12x & = &-4\\\Leftrightarrow & \color{red}{-12}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-5}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5-9x } & = & 13 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-20x & = &18\\\Leftrightarrow & \color{red}{-20}x & = &18\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{18}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)