Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9-x } & = & -9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &13x & = &-18\\\Leftrightarrow & \color{red}{13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+10}& = & 3 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10-12x } & = & 3 \color{red}{ +12x }\color{blue}{-10-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &-x & = &-7\\\Leftrightarrow & \color{red}{-}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+13}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-3x } & = & -15 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-28\\\Leftrightarrow & \color{red}{-11}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-28}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{28}{11} } & & \\ & V = \left\{ \frac{28}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-1}& = & 5 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1+2x } & = & 5 \color{red}{ -2x }\color{blue}{+1+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 5 \color{blue}{+1} \\\Leftrightarrow &17x & = &6\\\Leftrightarrow & \color{red}{17}x & = &6\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{6}{17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-15}& = & 14 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15-9x } & = & 14 \color{red}{ +9x }\color{blue}{+15-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &-7x & = &29\\\Leftrightarrow & \color{red}{-7}x & = &29\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{29}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{7} } & & \\ & V = \left\{ \frac{-29}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-7}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-x } & = & -5 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -5 \color{blue}{+7} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+15}& = & 15 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15+9x } & = & 15 \color{red}{ -9x }\color{blue}{-15+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & 15 \color{blue}{-15} \\\Leftrightarrow &23x & = &0\\\Leftrightarrow & \color{red}{23}x & = &0\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{0}{23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+9}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9-x } & = & -2 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &-15x & = &-11\\\Leftrightarrow & \color{red}{-15}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{11}{15} } & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+12}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12-5x } & = & -14 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -14 \color{blue}{-12} \\\Leftrightarrow &7x & = &-26\\\Leftrightarrow & \color{red}{7}x & = &-26\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-26}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{7} } & & \\ & V = \left\{ \frac{-26}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-x } & = & 9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+6}& = & 13 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6-10x } & = & 13 \color{red}{ +10x }\color{blue}{-6-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & 13 \color{blue}{-6} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+2}& = & -15 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2+2x } & = & -15 \color{red}{ -2x }\color{blue}{-2+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -15 \color{blue}{-2} \\\Leftrightarrow &17x & = &-17\\\Leftrightarrow & \color{red}{17}x & = &-17\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-17}{17} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)