Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-3}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-9x } & = & -12 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & -12 \color{blue}{+3} \\\Leftrightarrow &-7x & = &-9\\\Leftrightarrow & \color{red}{-7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-13}& = & 2 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-10x } & = & 2 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 2 \color{blue}{+13} \\\Leftrightarrow &-13x & = &15\\\Leftrightarrow & \color{red}{-13}x & = &15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+7}& = & 7 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+7}\color{blue}{-7-12x } & = & 7 \color{red}{ +12x }\color{blue}{-7-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &-x & = &0\\\Leftrightarrow & \color{red}{-}x & = &0\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{0}{-1} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-13}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13-9x } & = & -1 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -1 \color{blue}{+13} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-9}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-9}\color{blue}{+9-13x } & = & 12 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &-25x & = &21\\\Leftrightarrow & \color{red}{-25}x & = &21\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{21}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{25} } & & \\ & V = \left\{ \frac{-21}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+14}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-x } & = & -14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -14 \color{blue}{-14} \\\Leftrightarrow &-14x & = &-28\\\Leftrightarrow & \color{red}{-14}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-28}{-14} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+5}\color{blue}{-5-x } & = & 13 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 13 \color{blue}{-5} \\\Leftrightarrow &-13x & = &8\\\Leftrightarrow & \color{red}{-13}x & = &8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & -6 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -6 \color{blue}{+4} \\\Leftrightarrow &-11x & = &-2\\\Leftrightarrow & \color{red}{-11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-7}& = & -8 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7+5x } & = & -8 \color{red}{ -5x }\color{blue}{+7+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &6x & = &-1\\\Leftrightarrow & \color{red}{6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-1}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+2}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2-x } & = & 11 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 11 \color{blue}{-2} \\\Leftrightarrow &-16x & = &9\\\Leftrightarrow & \color{red}{-16}x & = &9\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{9}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{16} } & & \\ & V = \left\{ \frac{-9}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-4}& = & 3 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-4}\color{blue}{+4+3x } & = & 3 \color{red}{ -3x }\color{blue}{+4+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 3 \color{blue}{+4} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+14}& = & -4 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14+5x } & = & -4 \color{red}{ -5x }\color{blue}{-14+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &11x & = &-18\\\Leftrightarrow & \color{red}{11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)