Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-12}& = & 15 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12+9x } & = & 15 \color{red}{ -9x }\color{blue}{+12+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 15 \color{blue}{+12} \\\Leftrightarrow &14x & = &27\\\Leftrightarrow & \color{red}{14}x & = &27\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{27}{14} \\\Leftrightarrow & \color{green}{ x = \frac{27}{14} } & & \\ & V = \left\{ \frac{27}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-15}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{-15}\color{blue}{+15-13x } & = & -6 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &-12x & = &9\\\Leftrightarrow & \color{red}{-12}x & = &9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+5}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-x } & = & -6 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -6 \color{blue}{-5} \\\Leftrightarrow &-4x & = &-11\\\Leftrightarrow & \color{red}{-4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+7}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-x } & = & 7 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &-6x & = &0\\\Leftrightarrow & \color{red}{-6}x & = &0\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{0}{-6} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-5}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5-7x } & = & -14 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &3x & = &-9\\\Leftrightarrow & \color{red}{3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-9}{3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-11}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-5x } & = & 3 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &-14x & = &14\\\Leftrightarrow & \color{red}{-14}x & = &14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{14}{-14} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+14}& = & 12 \color{red}{ -2x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14+2x } & = & 12 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 13x \color{blue}{+2x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &15x & = &-2\\\Leftrightarrow & \color{red}{15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-15}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15-x } & = & 8 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 8 \color{blue}{+15} \\\Leftrightarrow &-9x & = &23\\\Leftrightarrow & \color{red}{-9}x & = &23\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{23}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{9} } & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+5}& = & 5 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5-2x } & = & 5 \color{red}{ +2x }\color{blue}{-5-2x } \\\Leftrightarrow & 7x \color{blue}{-2x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-4}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4-11x } & = & 7 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-12}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12-x } & = & -12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -12 \color{blue}{+12} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-15}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15+11x } & = & 6 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 6 \color{blue}{+15} \\\Leftrightarrow &23x & = &21\\\Leftrightarrow & \color{red}{23}x & = &21\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{21}{23} \\\Leftrightarrow & \color{green}{ x = \frac{21}{23} } & & \\ & V = \left\{ \frac{21}{23} \right\} & \\\end{align}\)