Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+11}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11-13x } & = & -14 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &-10x & = &-25\\\Leftrightarrow & \color{red}{-10}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-25}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-13}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13+13x } & = & -5 \color{red}{ -13x }\color{blue}{+13+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -5 \color{blue}{+13} \\\Leftrightarrow &23x & = &8\\\Leftrightarrow & \color{red}{23}x & = &8\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{8}{23} \\\Leftrightarrow & \color{green}{ x = \frac{8}{23} } & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-8}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8-11x } & = & 1 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & 3x \color{blue}{-11x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &-8x & = &9\\\Leftrightarrow & \color{red}{-8}x & = &9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+7}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-3x } & = & -2 \color{red}{ +3x }\color{blue}{-7-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -2 \color{blue}{-7} \\\Leftrightarrow &-x & = &-9\\\Leftrightarrow & \color{red}{-}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-9}{-1} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-x } & = & 7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5-x } & = & -1 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+3}& = & -12 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3+9x } & = & -12 \color{red}{ -9x }\color{blue}{-3+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &19x & = &-15\\\Leftrightarrow & \color{red}{19}x & = &-15\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-15}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{19} } & & \\ & V = \left\{ \frac{-15}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-3}& = & 8 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3+3x } & = & 8 \color{red}{ -3x }\color{blue}{+3+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 8 \color{blue}{+3} \\\Leftrightarrow &13x & = &11\\\Leftrightarrow & \color{red}{13}x & = &11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-7}& = & -5 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7+10x } & = & -5 \color{red}{ -10x }\color{blue}{+7+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -5 \color{blue}{+7} \\\Leftrightarrow &17x & = &2\\\Leftrightarrow & \color{red}{17}x & = &2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+3}& = & -15 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3-8x } & = & -15 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &-3x & = &-18\\\Leftrightarrow & \color{red}{-3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-18}{-3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-15}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-x } & = & 11 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &-10x & = &26\\\Leftrightarrow & \color{red}{-10}x & = &26\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{26}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+4}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x } & = & 14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 14 \color{blue}{-4} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)