Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-13}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13-13x } & = & 10 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &-7x & = &23\\\Leftrightarrow & \color{red}{-7}x & = &23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{7} } & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-2}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-2}\color{blue}{+2-x } & = & 8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &-14x & = &10\\\Leftrightarrow & \color{red}{-14}x & = &10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+7}& = & -14 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7+4x } & = & -14 \color{red}{ -4x }\color{blue}{-7+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &9x & = &-21\\\Leftrightarrow & \color{red}{9}x & = &-21\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-21}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+5}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+5}\color{blue}{-5-x } & = & -2 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -2 \color{blue}{-5} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-5}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x } & = & 14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &-6x & = &19\\\Leftrightarrow & \color{red}{-6}x & = &19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{6} } & & \\ & V = \left\{ \frac{-19}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+13}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13+13x } & = & 8 \color{red}{ -13x }\color{blue}{-13+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 8 \color{blue}{-13} \\\Leftrightarrow &23x & = &-5\\\Leftrightarrow & \color{red}{23}x & = &-5\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-5}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{23} } & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-12}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12+13x } & = & -11 \color{red}{ -13x }\color{blue}{+12+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -11 \color{blue}{+12} \\\Leftrightarrow &27x & = &1\\\Leftrightarrow & \color{red}{27}x & = &1\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{1}{27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{27} } & & \\ & V = \left\{ \frac{1}{27} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-6}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{-6}\color{blue}{+6-3x } & = & 10 \color{red}{ +3x }\color{blue}{+6-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & 10 \color{blue}{+6} \\\Leftrightarrow &-5x & = &16\\\Leftrightarrow & \color{red}{-5}x & = &16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+9}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{+9}\color{blue}{-9-11x } & = & -14 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & -x \color{blue}{-11x } & = & -14 \color{blue}{-9} \\\Leftrightarrow &-12x & = &-23\\\Leftrightarrow & \color{red}{-12}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-23}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{23}{12} } & & \\ & V = \left\{ \frac{23}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+4}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-5x } & = & 14 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 14 \color{blue}{-4} \\\Leftrightarrow &-3x & = &10\\\Leftrightarrow & \color{red}{-3}x & = &10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-14}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-x } & = & -14 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -14 \color{blue}{+14} \\\Leftrightarrow &-12x & = &0\\\Leftrightarrow & \color{red}{-12}x & = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-7}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-7}\color{blue}{+7-9x } & = & -13 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -13 \color{blue}{+7} \\\Leftrightarrow &-17x & = &-6\\\Leftrightarrow & \color{red}{-17}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)