Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-6}& = & 8 \color{red}{ -6x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6+6x } & = & 8 \color{red}{ -6x }\color{blue}{+6+6x } \\\Leftrightarrow & x \color{blue}{+6x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &7x & = &14\\\Leftrightarrow & \color{red}{7}x & = &14\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{14}{7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-11}& = & -5 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11-12x } & = & -5 \color{red}{ +12x }\color{blue}{+11-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -5 \color{blue}{+11} \\\Leftrightarrow &-x & = &6\\\Leftrightarrow & \color{red}{-}x & = &6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{6}{-1} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+5}& = & 5 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5+7x } & = & 5 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &19x & = &0\\\Leftrightarrow & \color{red}{19}x & = &0\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{0}{19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-2}& = & -4 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2+5x } & = & -4 \color{red}{ -5x }\color{blue}{+2+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -4 \color{blue}{+2} \\\Leftrightarrow &8x & = &-2\\\Leftrightarrow & \color{red}{8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-2}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2-x } & = & -15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -15 \color{blue}{+2} \\\Leftrightarrow &-9x & = &-13\\\Leftrightarrow & \color{red}{-9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-14}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14-x } & = & -5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -5 \color{blue}{+14} \\\Leftrightarrow &-13x & = &9\\\Leftrightarrow & \color{red}{-13}x & = &9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{-3}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3+11x } & = & -7 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -7 \color{blue}{+3} \\\Leftrightarrow &17x & = &-4\\\Leftrightarrow & \color{red}{17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+8}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & 13 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 13 \color{blue}{-8} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+7}& = & 7 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7+5x } & = & 7 \color{red}{ -5x }\color{blue}{-7+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &13x & = &0\\\Leftrightarrow & \color{red}{13}x & = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+1}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1-13x } & = & -3 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -3 \color{blue}{-1} \\\Leftrightarrow &-7x & = &-4\\\Leftrightarrow & \color{red}{-7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-7}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-x } & = & -13 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -13 \color{blue}{+7} \\\Leftrightarrow &-5x & = &-6\\\Leftrightarrow & \color{red}{-5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-x } & = & 13 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{-6} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)