Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-5}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-13x } & = & 14 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &-25x & = &19\\\Leftrightarrow & \color{red}{-25}x & = &19\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{19}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{25} } & & \\ & V = \left\{ \frac{-19}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+3}& = & 2 \color{red}{ -8x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3+8x } & = & 2 \color{red}{ -8x }\color{blue}{-3+8x } \\\Leftrightarrow & -11x \color{blue}{+8x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-8}& = & -2 \color{red}{ -8x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8+8x } & = & -2 \color{red}{ -8x }\color{blue}{+8+8x } \\\Leftrightarrow & -9x \color{blue}{+8x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &-x & = &6\\\Leftrightarrow & \color{red}{-}x & = &6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{6}{-1} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-1}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1-11x } & = & -6 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-9}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9-5x } & = & -1 \color{red}{ +5x }\color{blue}{+9-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & -1 \color{blue}{+9} \\\Leftrightarrow &-x & = &8\\\Leftrightarrow & \color{red}{-}x & = &8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{8}{-1} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-4}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4-13x } & = & 10 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & 10 \color{blue}{+4} \\\Leftrightarrow &-7x & = &14\\\Leftrightarrow & \color{red}{-7}x & = &14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{14}{-7} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+15}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15+7x } & = & 2 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & -4x \color{blue}{+7x } & = & 2 \color{blue}{-15} \\\Leftrightarrow &3x & = &-13\\\Leftrightarrow & \color{red}{3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+7}& = & -15 \color{red}{ -2x } \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7+2x } & = & -15 \color{red}{ -2x }\color{blue}{-7+2x } \\\Leftrightarrow & -7x \color{blue}{+2x } & = & -15 \color{blue}{-7} \\\Leftrightarrow &-5x & = &-22\\\Leftrightarrow & \color{red}{-5}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-3}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-3}\color{blue}{+3-x } & = & -5 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &-15x & = &-2\\\Leftrightarrow & \color{red}{-15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+15}& = & -6 \color{red}{ +15x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-15x } & = & -6 \color{red}{ +15x }\color{blue}{-15-15x } \\\Leftrightarrow & 2x \color{blue}{-15x } & = & -6 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-21\\\Leftrightarrow & \color{red}{-13}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-21}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{21}{13} } & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-4}& = & -9 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4-14x } & = & -9 \color{red}{ +14x }\color{blue}{+4-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & -9 \color{blue}{+4} \\\Leftrightarrow &-x & = &-5\\\Leftrightarrow & \color{red}{-}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-5}{-1} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+14}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-11x } & = & -4 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)