Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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