Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x } & = & -11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &-8x & = &2\\\Leftrightarrow & \color{red}{-8}x & = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12-x } & = & 10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-13}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13+11x } & = & 11 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & -x \color{blue}{+11x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &10x & = &24\\\Leftrightarrow & \color{red}{10}x & = &24\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{24}{10} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-12}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12-7x } & = & 6 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 6 \color{blue}{+12} \\\Leftrightarrow &8x & = &18\\\Leftrightarrow & \color{red}{8}x & = &18\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{18}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+13}& = & -10 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13+7x } & = & -10 \color{red}{ -7x }\color{blue}{-13+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &19x & = &-23\\\Leftrightarrow & \color{red}{19}x & = &-23\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-23}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{19} } & & \\ & V = \left\{ \frac{-23}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-10}& = & 13 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10-10x } & = & 13 \color{red}{ +10x }\color{blue}{+10-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &-3x & = &23\\\Leftrightarrow & \color{red}{-3}x & = &23\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{23}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{3} } & & \\ & V = \left\{ \frac{-23}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-14}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x } & = & -4 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -4 \color{blue}{+14} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-10}& = & 6 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10-14x } & = & 6 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & 6 \color{blue}{+10} \\\Leftrightarrow &-x & = &16\\\Leftrightarrow & \color{red}{-}x & = &16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{16}{-1} \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-3}& = & -2 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3+11x } & = & -2 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &17x & = &1\\\Leftrightarrow & \color{red}{17}x & = &1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-15}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15-13x } & = & -10 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & 7x \color{blue}{-13x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &-6x & = &5\\\Leftrightarrow & \color{red}{-6}x & = &5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+14}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x } & = & 15 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 15 \color{blue}{-14} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-4}& = & -14 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4+2x } & = & -14 \color{red}{ -2x }\color{blue}{+4+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &5x & = &-10\\\Leftrightarrow & \color{red}{5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-10}{5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)