Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{+14}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-3x } & = & -15 \color{red}{ +3x }\color{blue}{-14-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -15 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-29\\\Leftrightarrow & \color{red}{-5}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-29}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{29}{5} } & & \\ & V = \left\{ \frac{29}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x } & = & 12 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 12 \color{blue}{-12} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+10}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-x } & = & -1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &-10x & = &-11\\\Leftrightarrow & \color{red}{-10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+14}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14-9x } & = & 3 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &5x & = &-11\\\Leftrightarrow & \color{red}{5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+2}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2+3x } & = & 13 \color{red}{ -3x }\color{blue}{-2+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &13x & = &11\\\Leftrightarrow & \color{red}{13}x & = &11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+7}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-x } & = & -13 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &-11x & = &-20\\\Leftrightarrow & \color{red}{-11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-5}& = & -15 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5-12x } & = & -15 \color{red}{ +12x }\color{blue}{+5-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -15 \color{blue}{+5} \\\Leftrightarrow &-x & = &-10\\\Leftrightarrow & \color{red}{-}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-10}{-1} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-7}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-7}\color{blue}{+7-x } & = & 5 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+14}& = & -1 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14+3x } & = & -1 \color{red}{ -3x }\color{blue}{-14+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &7x & = &-15\\\Leftrightarrow & \color{red}{7}x & = &-15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-3}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-13x } & = & 14 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &-25x & = &17\\\Leftrightarrow & \color{red}{-25}x & = &17\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{17}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{25} } & & \\ & V = \left\{ \frac{-17}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+7}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-x } & = & 4 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &-15x & = &-3\\\Leftrightarrow & \color{red}{-15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{+7}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-7x } & = & 14 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 14 \color{blue}{-7} \\\Leftrightarrow &-17x & = &7\\\Leftrightarrow & \color{red}{-17}x & = &7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)