Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+12}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12-x } & = & -15 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &5x & = &-27\\\Leftrightarrow & \color{red}{5}x & = &-27\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-27}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{5} } & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-8}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-x } & = & -5 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-11}& = & -15 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11-10x } & = & -15 \color{red}{ +10x }\color{blue}{+11-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & -15 \color{blue}{+11} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+1}& = & -6 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1-8x } & = & -6 \color{red}{ +8x }\color{blue}{-1-8x } \\\Leftrightarrow & 13x \color{blue}{-8x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &5x & = &-7\\\Leftrightarrow & \color{red}{5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+14}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14-x } & = & -1 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &13x & = &-15\\\Leftrightarrow & \color{red}{13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+4}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4-x } & = & -1 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -1 \color{blue}{-4} \\\Leftrightarrow &13x & = &-5\\\Leftrightarrow & \color{red}{13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+6}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6-x } & = & -13 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -13 \color{blue}{-6} \\\Leftrightarrow &7x & = &-19\\\Leftrightarrow & \color{red}{7}x & = &-19\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-19}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-7}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7+11x } & = & 7 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 7 \color{blue}{+7} \\\Leftrightarrow &26x & = &14\\\Leftrightarrow & \color{red}{26}x & = &14\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{14}{26} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-15}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15+7x } & = & -2 \color{red}{ -7x }\color{blue}{+15+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &18x & = &13\\\Leftrightarrow & \color{red}{18}x & = &13\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{13}{18} \\\Leftrightarrow & \color{green}{ x = \frac{13}{18} } & & \\ & V = \left\{ \frac{13}{18} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-12}& = & -13 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12-2x } & = & -13 \color{red}{ +2x }\color{blue}{+12-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & -13 \color{blue}{+12} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+6}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-13x } & = & -6 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & -6 \color{blue}{-6} \\\Leftrightarrow &-18x & = &-12\\\Leftrightarrow & \color{red}{-18}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-12}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-11}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-x } & = & -2 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{+11} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)