Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+8}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8-13x } & = & 2 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &-8x & = &-6\\\Leftrightarrow & \color{red}{-8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+12}& = & 11 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12+13x } & = & 11 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &23x & = &-1\\\Leftrightarrow & \color{red}{23}x & = &-1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-4}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-4}\color{blue}{+4-5x } & = & -4 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -4 \color{blue}{+4} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-13}& = & -8 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13+5x } & = & -8 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &6x & = &5\\\Leftrightarrow & \color{red}{6}x & = &5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+2}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2+11x } & = & -13 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -13 \color{blue}{-2} \\\Leftrightarrow &14x & = &-15\\\Leftrightarrow & \color{red}{14}x & = &-15\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-15}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{14} } & & \\ & V = \left\{ \frac{-15}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+10}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10+11x } & = & 4 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 4 \color{blue}{-10} \\\Leftrightarrow &25x & = &-6\\\Leftrightarrow & \color{red}{25}x & = &-6\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-6}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{25} } & & \\ & V = \left\{ \frac{-6}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+1}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-x } & = & -11 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -11 \color{blue}{-1} \\\Leftrightarrow &-10x & = &-12\\\Leftrightarrow & \color{red}{-10}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-12}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+14}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-13x } & = & -1 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-19x & = &-15\\\Leftrightarrow & \color{red}{-19}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-15}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{15}{19} } & & \\ & V = \left\{ \frac{15}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+3}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-7x } & = & 1 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 1 \color{blue}{-3} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-15}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-7x } & = & -13 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -13 \color{blue}{+15} \\\Leftrightarrow &-20x & = &2\\\Leftrightarrow & \color{red}{-20}x & = &2\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{2}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+2}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-5x } & = & -9 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -9 \color{blue}{-2} \\\Leftrightarrow &-14x & = &-11\\\Leftrightarrow & \color{red}{-14}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{11}{14} } & & \\ & V = \left\{ \frac{11}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15-x } & = & 12 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &11x & = &27\\\Leftrightarrow & \color{red}{11}x & = &27\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{27}{11} \\\Leftrightarrow & \color{green}{ x = \frac{27}{11} } & & \\ & V = \left\{ \frac{27}{11} \right\} & \\\end{align}\)