Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+12}& = & 12 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12+8x } & = & 12 \color{red}{ -8x }\color{blue}{-12+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 12 \color{blue}{-12} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+13}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13-11x } & = & 3 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & 3 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+8}& = & 3 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8+8x } & = & 3 \color{red}{ -8x }\color{blue}{-8+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 3 \color{blue}{-8} \\\Leftrightarrow &17x & = &-5\\\Leftrightarrow & \color{red}{17}x & = &-5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{17} } & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-x } & = & 12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &-10x & = &24\\\Leftrightarrow & \color{red}{-10}x & = &24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-7}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7-11x } & = & 6 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & 6 \color{blue}{+7} \\\Leftrightarrow &3x & = &13\\\Leftrightarrow & \color{red}{3}x & = &13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+12}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12-11x } & = & -10 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &-21x & = &-22\\\Leftrightarrow & \color{red}{-21}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-22}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{22}{21} } & & \\ & V = \left\{ \frac{22}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+13}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13+13x } & = & -5 \color{red}{ -13x }\color{blue}{-13+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &24x & = &-18\\\Leftrightarrow & \color{red}{24}x & = &-18\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-18}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+13}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-x } & = & 6 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-15}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-x } & = & 9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &-8x & = &24\\\Leftrightarrow & \color{red}{-8}x & = &24\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{24}{-8} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2-x } & = & 15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &5x & = &13\\\Leftrightarrow & \color{red}{5}x & = &13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+6}& = & -9 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6+13x } & = & -9 \color{red}{ -13x }\color{blue}{-6+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &12x & = &-15\\\Leftrightarrow & \color{red}{12}x & = &-15\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-15}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-9}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9-x } & = & 12 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &-12x & = &21\\\Leftrightarrow & \color{red}{-12}x & = &21\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{21}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)