Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14-x } & = & -8 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -8 \color{blue}{-14} \\\Leftrightarrow &7x & = &-22\\\Leftrightarrow & \color{red}{7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-8}& = & 6 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8+7x } & = & 6 \color{red}{ -7x }\color{blue}{+8+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 6 \color{blue}{+8} \\\Leftrightarrow &11x & = &14\\\Leftrightarrow & \color{red}{11}x & = &14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{14}{11} } & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+13}& = & -1 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13-12x } & = & -1 \color{red}{ +12x }\color{blue}{-13-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-14\\\Leftrightarrow & \color{red}{-13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-10}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-x } & = & -7 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-16x & = &3\\\Leftrightarrow & \color{red}{-16}x & = &3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{16} } & & \\ & V = \left\{ \frac{-3}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14-x } & = & -8 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -8 \color{blue}{-14} \\\Leftrightarrow &13x & = &-22\\\Leftrightarrow & \color{red}{13}x & = &-22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{13} } & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+14}& = & -6 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-14x } & = & -6 \color{red}{ +14x }\color{blue}{-14-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &-23x & = &-20\\\Leftrightarrow & \color{red}{-23}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-20}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{20}{23} } & & \\ & V = \left\{ \frac{20}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-13}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13-9x } & = & 5 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 5 \color{blue}{+13} \\\Leftrightarrow &-x & = &18\\\Leftrightarrow & \color{red}{-}x & = &18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{18}{-1} \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+1}& = & 3 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1+3x } & = & 3 \color{red}{ -3x }\color{blue}{-1+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &10x & = &2\\\Leftrightarrow & \color{red}{10}x & = &2\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{2}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+5}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+5}\color{blue}{-5-x } & = & 8 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 8 \color{blue}{-5} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+6}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6-13x } & = & 14 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & 14 \color{blue}{-6} \\\Leftrightarrow &-12x & = &8\\\Leftrightarrow & \color{red}{-12}x & = &8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-12}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12-9x } & = & 13 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &5x & = &25\\\Leftrightarrow & \color{red}{5}x & = &25\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{25}{5} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+2}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-9x } & = & 8 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 8 \color{blue}{-2} \\\Leftrightarrow &-17x & = &6\\\Leftrightarrow & \color{red}{-17}x & = &6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)