Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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