Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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