Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-6}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6-7x } & = & 1 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &-17x & = &7\\\Leftrightarrow & \color{red}{-17}x & = &7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-x } & = & 13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-14}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14-x } & = & 8 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 8 \color{blue}{+14} \\\Leftrightarrow &12x & = &22\\\Leftrightarrow & \color{red}{12}x & = &22\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{22}{12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+5}& = & -8 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5-3x } & = & -8 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &11x & = &-13\\\Leftrightarrow & \color{red}{11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-13}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-5}& = & 2 \color{red}{ +2x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5-2x } & = & 2 \color{red}{ +2x }\color{blue}{+5-2x } \\\Leftrightarrow & 5x \color{blue}{-2x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &3x & = &7\\\Leftrightarrow & \color{red}{3}x & = &7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+14}& = & 10 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14+2x } & = & 10 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-3}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-x } & = & 10 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &-13x & = &13\\\Leftrightarrow & \color{red}{-13}x & = &13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{13}{-13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-3}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-x } & = & 8 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 8 \color{blue}{+3} \\\Leftrightarrow &-10x & = &11\\\Leftrightarrow & \color{red}{-10}x & = &11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-9}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-9x } & = & 3 \color{red}{ +9x }\color{blue}{+9-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 3 \color{blue}{+9} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-7}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7-x } & = & 15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &-12x & = &22\\\Leftrightarrow & \color{red}{-12}x & = &22\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{22}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-13}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13-x } & = & 13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &-5x & = &26\\\Leftrightarrow & \color{red}{-5}x & = &26\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{26}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{5} } & & \\ & V = \left\{ \frac{-26}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+1}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-x } & = & 1 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 1 \color{blue}{-1} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)