Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-3}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-5x } & = & 1 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 1 \color{blue}{+3} \\\Leftrightarrow &7x & = &4\\\Leftrightarrow & \color{red}{7}x & = &4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+14}& = & -8 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14+3x } & = & -8 \color{red}{ -3x }\color{blue}{-14+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -8 \color{blue}{-14} \\\Leftrightarrow &13x & = &-22\\\Leftrightarrow & \color{red}{13}x & = &-22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{13} } & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-9}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9+13x } & = & 13 \color{red}{ -13x }\color{blue}{+9+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &22x & = &22\\\Leftrightarrow & \color{red}{22}x & = &22\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{22}{22} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-15}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-13x } & = & 9 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &-28x & = &24\\\Leftrightarrow & \color{red}{-28}x & = &24\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{24}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+14}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14-x } & = & 15 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 15 \color{blue}{-14} \\\Leftrightarrow &12x & = &1\\\Leftrightarrow & \color{red}{12}x & = &1\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{1}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+14}& = & 1 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14-10x } & = & 1 \color{red}{ +10x }\color{blue}{-14-10x } \\\Leftrightarrow & x \color{blue}{-10x } & = & 1 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-13\\\Leftrightarrow & \color{red}{-9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+6}& = & 15 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6-4x } & = & 15 \color{red}{ +4x }\color{blue}{-6-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-9}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9-13x } & = & 6 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &-4x & = &15\\\Leftrightarrow & \color{red}{-4}x & = &15\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{15}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{4} } & & \\ & V = \left\{ \frac{-15}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-4}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & 7 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &-11x & = &11\\\Leftrightarrow & \color{red}{-11}x & = &11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{11}{-11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+13}& = & -5 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13+5x } & = & -5 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &16x & = &-18\\\Leftrightarrow & \color{red}{16}x & = &-18\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-18}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+15}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15+13x } & = & -13 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &27x & = &-28\\\Leftrightarrow & \color{red}{27}x & = &-28\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-28}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{27} } & & \\ & V = \left\{ \frac{-28}{27} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-10}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-7x } & = & 12 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &-16x & = &22\\\Leftrightarrow & \color{red}{-16}x & = &22\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{22}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)