Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-8}& = & -7 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8-8x } & = & -7 \color{red}{ +8x }\color{blue}{+8-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & -7 \color{blue}{+8} \\\Leftrightarrow &-3x & = &1\\\Leftrightarrow & \color{red}{-3}x & = &1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-x } & = & 2 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 2 \color{blue}{-5} \\\Leftrightarrow &-4x & = &-3\\\Leftrightarrow & \color{red}{-4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-15}& = & -9 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-12x } & = & -9 \color{red}{ +12x }\color{blue}{+15-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -9 \color{blue}{+15} \\\Leftrightarrow &-x & = &6\\\Leftrightarrow & \color{red}{-}x & = &6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{6}{-1} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-3}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-x } & = & 6 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 6 \color{blue}{+3} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+12}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12-13x } & = & 15 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-8}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8-3x } & = & 10 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+7}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7+2x } & = & 2 \color{red}{ -2x }\color{blue}{-7+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & 2 \color{blue}{-7} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & 14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+1}& = & 2 \color{red}{ -14x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1+14x } & = & 2 \color{red}{ -14x }\color{blue}{-1+14x } \\\Leftrightarrow & -x \color{blue}{+14x } & = & 2 \color{blue}{-1} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+15}& = & 15 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15+8x } & = & 15 \color{red}{ -8x }\color{blue}{-15+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 15 \color{blue}{-15} \\\Leftrightarrow &17x & = &0\\\Leftrightarrow & \color{red}{17}x & = &0\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{0}{17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-8}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8+11x } & = & 4 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &26x & = &12\\\Leftrightarrow & \color{red}{26}x & = &12\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{12}{26} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+15}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-x } & = & 14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)