Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+7}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+7}\color{blue}{-7+11x } & = & -14 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &14x & = &-21\\\Leftrightarrow & \color{red}{14}x & = &-21\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-21}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & 13 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{-9} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-12}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12-11x } & = & -9 \color{red}{ +11x }\color{blue}{+12-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & -9 \color{blue}{+12} \\\Leftrightarrow &3x & = &3\\\Leftrightarrow & \color{red}{3}x & = &3\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{3}{3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+5}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-3x } & = & 1 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & 1 \color{blue}{-5} \\\Leftrightarrow &-5x & = &-4\\\Leftrightarrow & \color{red}{-5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+7}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7-5x } & = & -5 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -5 \color{blue}{-7} \\\Leftrightarrow &7x & = &-12\\\Leftrightarrow & \color{red}{7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+13}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13-3x } & = & 11 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &-14x & = &-2\\\Leftrightarrow & \color{red}{-14}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+14}& = & 11 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14-6x } & = & 11 \color{red}{ +6x }\color{blue}{-14-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 11 \color{blue}{-14} \\\Leftrightarrow &-17x & = &-3\\\Leftrightarrow & \color{red}{-17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+3}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-13x } & = & 14 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &-25x & = &11\\\Leftrightarrow & \color{red}{-25}x & = &11\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{11}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{25} } & & \\ & V = \left\{ \frac{-11}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+5}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5-7x } & = & 3 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &-x & = &-2\\\Leftrightarrow & \color{red}{-}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-2}{-1} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9-x } & = & -9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &-12x & = &0\\\Leftrightarrow & \color{red}{-12}x & = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+9}& = & 7 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9+9x } & = & 7 \color{red}{ -9x }\color{blue}{-9+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & 7 \color{blue}{-9} \\\Leftrightarrow &23x & = &-2\\\Leftrightarrow & \color{red}{23}x & = &-2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{23} } & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-9}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{-9}\color{blue}{+9-7x } & = & 10 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &-x & = &19\\\Leftrightarrow & \color{red}{-}x & = &19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{19}{-1} \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)