Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-8}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-13x } & = & 12 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &x & = &20\\\Leftrightarrow & \color{red}{}x & = &20\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 20 \\\Leftrightarrow & \color{green}{ x = 20 } & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-3}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-x } & = & 14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &-8x & = &17\\\Leftrightarrow & \color{red}{-8}x & = &17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{8} } & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-2}& = & -12 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2+11x } & = & -12 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -12 \color{blue}{+2} \\\Leftrightarrow &17x & = &-10\\\Leftrightarrow & \color{red}{17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+2}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-7x } & = & -15 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -15 \color{blue}{-2} \\\Leftrightarrow &-13x & = &-17\\\Leftrightarrow & \color{red}{-13}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+1}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1-x } & = & 1 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 1 \color{blue}{-1} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+12}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+12}\color{blue}{-12+11x } & = & 2 \color{red}{ -11x }\color{blue}{-12+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &26x & = &-10\\\Leftrightarrow & \color{red}{26}x & = &-10\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-10}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-2}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2-13x } & = & -5 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &-15x & = &-3\\\Leftrightarrow & \color{red}{-15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+5}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-x } & = & 5 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &-16x & = &0\\\Leftrightarrow & \color{red}{-16}x & = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-x } & = & -12 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -12 \color{blue}{+1} \\\Leftrightarrow &-13x & = &-11\\\Leftrightarrow & \color{red}{-13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-12}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+2x } & = & 2 \color{red}{ -2x }\color{blue}{+12+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &5x & = &14\\\Leftrightarrow & \color{red}{5}x & = &14\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{14}{5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-x } & = & -8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &-8x & = &-23\\\Leftrightarrow & \color{red}{-8}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-23}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{23}{8} } & & \\ & V = \left\{ \frac{23}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+5}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5-7x } & = & -5 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & 13x \color{blue}{-7x } & = & -5 \color{blue}{-5} \\\Leftrightarrow &6x & = &-10\\\Leftrightarrow & \color{red}{6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-10}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)