Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+13}& = & 3 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13+12x } & = & 3 \color{red}{ -12x }\color{blue}{-13+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 3 \color{blue}{-13} \\\Leftrightarrow &25x & = &-10\\\Leftrightarrow & \color{red}{25}x & = &-10\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-10}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-7}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7+7x } & = & 15 \color{red}{ -7x }\color{blue}{+7+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &19x & = &22\\\Leftrightarrow & \color{red}{19}x & = &22\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{22}{19} \\\Leftrightarrow & \color{green}{ x = \frac{22}{19} } & & \\ & V = \left\{ \frac{22}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-6}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6-13x } & = & -8 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -8 \color{blue}{+6} \\\Leftrightarrow &-x & = &-2\\\Leftrightarrow & \color{red}{-}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-2}{-1} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-14}& = & 11 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14+14x } & = & 11 \color{red}{ -14x }\color{blue}{+14+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 11 \color{blue}{+14} \\\Leftrightarrow &19x & = &25\\\Leftrightarrow & \color{red}{19}x & = &25\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{25}{19} \\\Leftrightarrow & \color{green}{ x = \frac{25}{19} } & & \\ & V = \left\{ \frac{25}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-15}& = & 1 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+2x } & = & 1 \color{red}{ -2x }\color{blue}{+15+2x } \\\Leftrightarrow & 7x \color{blue}{+2x } & = & 1 \color{blue}{+15} \\\Leftrightarrow &9x & = &16\\\Leftrightarrow & \color{red}{9}x & = &16\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{16}{9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+13}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-x } & = & 5 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 5 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-8\\\Leftrightarrow & \color{red}{-13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+15}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15-7x } & = & -10 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -10 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-25\\\Leftrightarrow & \color{red}{-13}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-25}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{25}{13} } & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-10}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-11x } & = & 5 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 5 \color{blue}{+10} \\\Leftrightarrow &-18x & = &15\\\Leftrightarrow & \color{red}{-18}x & = &15\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{15}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+14}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x } & = & 6 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 6 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-4}& = & -8 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4-10x } & = & -8 \color{red}{ +10x }\color{blue}{+4-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &-7x & = &-4\\\Leftrightarrow & \color{red}{-7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-15}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15-11x } & = & 10 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &-5x & = &25\\\Leftrightarrow & \color{red}{-5}x & = &25\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{25}{-5} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-15}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15-x } & = & 9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &x & = &24\\\Leftrightarrow & \color{red}{}x & = &24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 24 \\\Leftrightarrow & \color{green}{ x = 24 } & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)