Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-12}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-x } & = & -1 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -1 \color{blue}{+12} \\\Leftrightarrow &-16x & = &11\\\Leftrightarrow & \color{red}{-16}x & = &11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{16} } & & \\ & V = \left\{ \frac{-11}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-6}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6-13x } & = & 11 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &-9x & = &17\\\Leftrightarrow & \color{red}{-9}x & = &17\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{17}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{9} } & & \\ & V = \left\{ \frac{-17}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-14}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14-x } & = & -11 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -11 \color{blue}{+14} \\\Leftrightarrow &5x & = &3\\\Leftrightarrow & \color{red}{5}x & = &3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+13}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13-9x } & = & 2 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 2 \color{blue}{-13} \\\Leftrightarrow &-x & = &-11\\\Leftrightarrow & \color{red}{-}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-11}{-1} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+7}& = & -12 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7+10x } & = & -12 \color{red}{ -10x }\color{blue}{-7+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &9x & = &-19\\\Leftrightarrow & \color{red}{9}x & = &-19\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-19}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-6}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6-7x } & = & 1 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &5x & = &7\\\Leftrightarrow & \color{red}{5}x & = &7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+12}& = & -3 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12+3x } & = & -3 \color{red}{ -3x }\color{blue}{-12+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -3 \color{blue}{-12} \\\Leftrightarrow &10x & = &-15\\\Leftrightarrow & \color{red}{10}x & = &-15\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-15}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-4}& = & -11 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4+8x } & = & -11 \color{red}{ -8x }\color{blue}{+4+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -11 \color{blue}{+4} \\\Leftrightarrow &11x & = &-7\\\Leftrightarrow & \color{red}{11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-4}& = & 14 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4+11x } & = & 14 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 14 \color{blue}{+4} \\\Leftrightarrow &17x & = &18\\\Leftrightarrow & \color{red}{17}x & = &18\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{18}{17} \\\Leftrightarrow & \color{green}{ x = \frac{18}{17} } & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-12}& = & 9 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-9x } & = & 9 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &-11x & = &21\\\Leftrightarrow & \color{red}{-11}x & = &21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-5}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5-x } & = & 10 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 10 \color{blue}{+5} \\\Leftrightarrow &6x & = &15\\\Leftrightarrow & \color{red}{6}x & = &15\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{15}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-10}& = & -14 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10+12x } & = & -14 \color{red}{ -12x }\color{blue}{+10+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & -14 \color{blue}{+10} \\\Leftrightarrow &17x & = &-4\\\Leftrightarrow & \color{red}{17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)