Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-5}& = & 5 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{-5}\color{blue}{+5+8x } & = & 5 \color{red}{ -8x }\color{blue}{+5+8x } \\\Leftrightarrow & x \color{blue}{+8x } & = & 5 \color{blue}{+5} \\\Leftrightarrow &9x & = &10\\\Leftrightarrow & \color{red}{9}x & = &10\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{10}{9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+15}& = & 4 \color{red}{ -12x } \\\Leftrightarrow & x \color{red}{+15}\color{blue}{-15+12x } & = & 4 \color{red}{ -12x }\color{blue}{-15+12x } \\\Leftrightarrow & x \color{blue}{+12x } & = & 4 \color{blue}{-15} \\\Leftrightarrow &13x & = &-11\\\Leftrightarrow & \color{red}{13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-9}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9-11x } & = & 5 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & 5 \color{blue}{+9} \\\Leftrightarrow &-x & = &14\\\Leftrightarrow & \color{red}{-}x & = &14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{14}{-1} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-6}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-9x } & = & 13 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &-7x & = &19\\\Leftrightarrow & \color{red}{-7}x & = &19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6-x } & = & 3 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 3 \color{blue}{-6} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+9}& = & -5 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9+5x } & = & -5 \color{red}{ -5x }\color{blue}{-9+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &11x & = &-14\\\Leftrightarrow & \color{red}{11}x & = &-14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+12}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12-13x } & = & 9 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &-7x & = &-3\\\Leftrightarrow & \color{red}{-7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+5}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-11x } & = & 5 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &-21x & = &0\\\Leftrightarrow & \color{red}{-21}x & = &0\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{0}{-21} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+15}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-11x } & = & -13 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &-3x & = &-28\\\Leftrightarrow & \color{red}{-3}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-28}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{28}{3} } & & \\ & V = \left\{ \frac{28}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-3}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3-x } & = & -3 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -3 \color{blue}{+3} \\\Leftrightarrow &13x & = &0\\\Leftrightarrow & \color{red}{13}x & = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-7}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-7}\color{blue}{+7-11x } & = & 6 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 6 \color{blue}{+7} \\\Leftrightarrow &-7x & = &13\\\Leftrightarrow & \color{red}{-7}x & = &13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-8}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8-x } & = & 13 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 13 \color{blue}{+8} \\\Leftrightarrow &-4x & = &21\\\Leftrightarrow & \color{red}{-4}x & = &21\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{21}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{4} } & & \\ & V = \left\{ \frac{-21}{4} \right\} & \\\end{align}\)