Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+9}& = & -12 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-3x } & = & -12 \color{red}{ +3x }\color{blue}{-9-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -12 \color{blue}{-9} \\\Leftrightarrow &-14x & = &-21\\\Leftrightarrow & \color{red}{-14}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-21}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-x } & = & -9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-x } & = & 9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &-13x & = &10\\\Leftrightarrow & \color{red}{-13}x & = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-8}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8-x } & = & 5 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 5 \color{blue}{+8} \\\Leftrightarrow &4x & = &13\\\Leftrightarrow & \color{red}{4}x & = &13\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{13}{4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+5}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5+13x } & = & 9 \color{red}{ -13x }\color{blue}{-5+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 9 \color{blue}{-5} \\\Leftrightarrow &20x & = &4\\\Leftrightarrow & \color{red}{20}x & = &4\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{4}{20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+2}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & -12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -12 \color{blue}{-2} \\\Leftrightarrow &-15x & = &-14\\\Leftrightarrow & \color{red}{-15}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-12}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12-x } & = & -5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-2}& = & 8 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2-3x } & = & 8 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &-17x & = &10\\\Leftrightarrow & \color{red}{-17}x & = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-12}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12-x } & = & -5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-13}& = & 3 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13+14x } & = & 3 \color{red}{ -14x }\color{blue}{+13+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & 3 \color{blue}{+13} \\\Leftrightarrow &17x & = &16\\\Leftrightarrow & \color{red}{17}x & = &16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+5}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5-5x } & = & -9 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-9x & = &-14\\\Leftrightarrow & \color{red}{-9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-4}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4-x } & = & 12 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &-8x & = &16\\\Leftrightarrow & \color{red}{-8}x & = &16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{16}{-8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)