Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-8}& = & 14 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8+8x } & = & 14 \color{red}{ -8x }\color{blue}{+8+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 14 \color{blue}{+8} \\\Leftrightarrow &19x & = &22\\\Leftrightarrow & \color{red}{19}x & = &22\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{22}{19} \\\Leftrightarrow & \color{green}{ x = \frac{22}{19} } & & \\ & V = \left\{ \frac{22}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-7}& = & 13 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7+2x } & = & 13 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 13 \color{blue}{+7} \\\Leftrightarrow &5x & = &20\\\Leftrightarrow & \color{red}{5}x & = &20\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{20}{5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+13}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13-x } & = & -6 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -6 \color{blue}{-13} \\\Leftrightarrow &-4x & = &-19\\\Leftrightarrow & \color{red}{-4}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-14}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14+11x } & = & 2 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &25x & = &16\\\Leftrightarrow & \color{red}{25}x & = &16\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{16}{25} \\\Leftrightarrow & \color{green}{ x = \frac{16}{25} } & & \\ & V = \left\{ \frac{16}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-14}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14-x } & = & -1 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &-3x & = &13\\\Leftrightarrow & \color{red}{-3}x & = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-6}& = & 13 \color{red}{ +15x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6-15x } & = & 13 \color{red}{ +15x }\color{blue}{+6-15x } \\\Leftrightarrow & x \color{blue}{-15x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &-14x & = &19\\\Leftrightarrow & \color{red}{-14}x & = &19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{14} } & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-10}& = & -6 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-3x } & = & -6 \color{red}{ +3x }\color{blue}{+10-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -6 \color{blue}{+10} \\\Leftrightarrow &-x & = &4\\\Leftrightarrow & \color{red}{-}x & = &4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{4}{-1} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-9}& = & 10 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9+6x } & = & 10 \color{red}{ -6x }\color{blue}{+9+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &19x & = &19\\\Leftrightarrow & \color{red}{19}x & = &19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{19}{19} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+13}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-x } & = & -10 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &-6x & = &-23\\\Leftrightarrow & \color{red}{-6}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-23}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{23}{6} } & & \\ & V = \left\{ \frac{23}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & -7 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -7 \color{blue}{+6} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-3}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-3}\color{blue}{+3+7x } & = & -3 \color{red}{ -7x }\color{blue}{+3+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -3 \color{blue}{+3} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-13}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13+7x } & = & 2 \color{red}{ -7x }\color{blue}{+13+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 2 \color{blue}{+13} \\\Leftrightarrow &15x & = &15\\\Leftrightarrow & \color{red}{15}x & = &15\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{15}{15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)