Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+12}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-9x } & = & 10 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &-17x & = &-2\\\Leftrightarrow & \color{red}{-17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+7}& = & 7 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7+5x } & = & 7 \color{red}{ -5x }\color{blue}{-7+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &6x & = &0\\\Leftrightarrow & \color{red}{6}x & = &0\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{0}{6} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-4}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-x } & = & 6 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 6 \color{blue}{+4} \\\Leftrightarrow &-16x & = &10\\\Leftrightarrow & \color{red}{-16}x & = &10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-3}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3-9x } & = & 10 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &-13x & = &13\\\Leftrightarrow & \color{red}{-13}x & = &13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{13}{-13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+5}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5-13x } & = & -8 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &-x & = &-13\\\Leftrightarrow & \color{red}{-}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-13}{-1} \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-3}& = & 2 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-10x } & = & 2 \color{red}{ +10x }\color{blue}{+3-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & 9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 9 \color{blue}{+9} \\\Leftrightarrow &-6x & = &18\\\Leftrightarrow & \color{red}{-6}x & = &18\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{18}{-6} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+12}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-5x } & = & 8 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 8 \color{blue}{-12} \\\Leftrightarrow &-7x & = &-4\\\Leftrightarrow & \color{red}{-7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-12}& = & 12 \color{red}{ +3x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12-3x } & = & 12 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & 11x \color{blue}{-3x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &8x & = &24\\\Leftrightarrow & \color{red}{8}x & = &24\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{24}{8} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+12}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12-11x } & = & -12 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & -12 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-24\\\Leftrightarrow & \color{red}{-3}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-24}{-3} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6-x } & = & -3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &7x & = &3\\\Leftrightarrow & \color{red}{7}x & = &3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+3}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-5x } & = & -15 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & -7x \color{blue}{-5x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &-12x & = &-18\\\Leftrightarrow & \color{red}{-12}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-18}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)