Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-11}& = & 8 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11+7x } & = & 8 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & 8 \color{blue}{+11} \\\Leftrightarrow &12x & = &19\\\Leftrightarrow & \color{red}{12}x & = &19\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{19}{12} \\\Leftrightarrow & \color{green}{ x = \frac{19}{12} } & & \\ & V = \left\{ \frac{19}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-5}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5+13x } & = & 3 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &21x & = &8\\\Leftrightarrow & \color{red}{21}x & = &8\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{8}{21} \\\Leftrightarrow & \color{green}{ x = \frac{8}{21} } & & \\ & V = \left\{ \frac{8}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+8}& = & 2 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8-12x } & = & 2 \color{red}{ +12x }\color{blue}{-8-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &-13x & = &-6\\\Leftrightarrow & \color{red}{-13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-6}& = & -7 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6-12x } & = & -7 \color{red}{ +12x }\color{blue}{+6-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & -7 \color{blue}{+6} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-10}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10-x } & = & 8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 8 \color{blue}{+10} \\\Leftrightarrow &-15x & = &18\\\Leftrightarrow & \color{red}{-15}x & = &18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-x } & = & 5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &-7x & = &17\\\Leftrightarrow & \color{red}{-7}x & = &17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-4}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4+13x } & = & 12 \color{red}{ -13x }\color{blue}{+4+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &27x & = &16\\\Leftrightarrow & \color{red}{27}x & = &16\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{16}{27} \\\Leftrightarrow & \color{green}{ x = \frac{16}{27} } & & \\ & V = \left\{ \frac{16}{27} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-14}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & -14 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -14 \color{blue}{+14} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+9}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-13x } & = & -5 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &-28x & = &-14\\\Leftrightarrow & \color{red}{-28}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-14}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-15}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15+7x } & = & 2 \color{red}{ -7x }\color{blue}{+15+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 2 \color{blue}{+15} \\\Leftrightarrow &11x & = &17\\\Leftrightarrow & \color{red}{11}x & = &17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+12}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-x } & = & -7 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -7 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-19\\\Leftrightarrow & \color{red}{-5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-6}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-13x } & = & 6 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &-17x & = &12\\\Leftrightarrow & \color{red}{-17}x & = &12\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{12}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)