Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-14}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14-5x } & = & -1 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &7x & = &13\\\Leftrightarrow & \color{red}{7}x & = &13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-8}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x } & = & -5 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-x } & = & 5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 5 \color{blue}{+14} \\\Leftrightarrow &-14x & = &19\\\Leftrightarrow & \color{red}{-14}x & = &19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{14} } & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+2}& = & 6 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+2}\color{blue}{-2-14x } & = & 6 \color{red}{ +14x }\color{blue}{-2-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &-27x & = &4\\\Leftrightarrow & \color{red}{-27}x & = &4\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{4}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{27} } & & \\ & V = \left\{ \frac{-4}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+14}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14+11x } & = & -7 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &20x & = &-21\\\Leftrightarrow & \color{red}{20}x & = &-21\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-21}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{20} } & & \\ & V = \left\{ \frac{-21}{20} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-9}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-9}\color{blue}{+9-x } & = & 15 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &-8x & = &24\\\Leftrightarrow & \color{red}{-8}x & = &24\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{24}{-8} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-13}& = & 9 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13-6x } & = & 9 \color{red}{ +6x }\color{blue}{+13-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & 9 \color{blue}{+13} \\\Leftrightarrow &-5x & = &22\\\Leftrightarrow & \color{red}{-5}x & = &22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{5} } & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+2}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-13x } & = & 3 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 3 \color{blue}{-2} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+5}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-7x } & = & 11 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &-17x & = &6\\\Leftrightarrow & \color{red}{-17}x & = &6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{-5}& = & -10 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5+14x } & = & -10 \color{red}{ -14x }\color{blue}{+5+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -10 \color{blue}{+5} \\\Leftrightarrow &29x & = &-5\\\Leftrightarrow & \color{red}{29}x & = &-5\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-5}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{29} } & & \\ & V = \left\{ \frac{-5}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+13}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13-7x } & = & 3 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & 3 \color{blue}{-13} \\\Leftrightarrow &-16x & = &-10\\\Leftrightarrow & \color{red}{-16}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-5}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-9x } & = & 13 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-7x & = &18\\\Leftrightarrow & \color{red}{-7}x & = &18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)