Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+2}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2-x } & = & -5 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -5 \color{blue}{-2} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-9}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9+11x } & = & -11 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &23x & = &-2\\\Leftrightarrow & \color{red}{23}x & = &-2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{23} } & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-13}& = & -3 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13-10x } & = & -3 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & x \color{blue}{-10x } & = & -3 \color{blue}{+13} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-15}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15-x } & = & 11 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &-13x & = &26\\\Leftrightarrow & \color{red}{-13}x & = &26\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{26}{-13} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+2}& = & 2 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2-12x } & = & 2 \color{red}{ +12x }\color{blue}{-2-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 2 \color{blue}{-2} \\\Leftrightarrow &-x & = &0\\\Leftrightarrow & \color{red}{-}x & = &0\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{0}{-1} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-2}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2-9x } & = & 2 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 2 \color{blue}{+2} \\\Leftrightarrow &-17x & = &4\\\Leftrightarrow & \color{red}{-17}x & = &4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+6}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-x } & = & -8 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -8 \color{blue}{-6} \\\Leftrightarrow &-7x & = &-14\\\Leftrightarrow & \color{red}{-7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-14}{-7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-14}& = & 14 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14-9x } & = & 14 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &5x & = &28\\\Leftrightarrow & \color{red}{5}x & = &28\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{28}{5} \\\Leftrightarrow & \color{green}{ x = \frac{28}{5} } & & \\ & V = \left\{ \frac{28}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+9}\color{blue}{-9-x } & = & -7 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -7 \color{blue}{-9} \\\Leftrightarrow &-4x & = &-16\\\Leftrightarrow & \color{red}{-4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-16}{-4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+6}& = & -3 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-9x } & = & -3 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-9}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-x } & = & -1 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -1 \color{blue}{+9} \\\Leftrightarrow &-10x & = &8\\\Leftrightarrow & \color{red}{-10}x & = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+3}& = & 14 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-4x } & = & 14 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &-11x & = &11\\\Leftrightarrow & \color{red}{-11}x & = &11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{11}{-11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)