Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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