Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+2}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-x } & = & -8 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -8 \color{blue}{-2} \\\Leftrightarrow &-11x & = &-10\\\Leftrightarrow & \color{red}{-11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+11}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11-x } & = & -2 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -2 \color{blue}{-11} \\\Leftrightarrow &-12x & = &-13\\\Leftrightarrow & \color{red}{-12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-5}\color{blue}{+5-x } & = & -9 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &-4x & = &-4\\\Leftrightarrow & \color{red}{-4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+11}& = & -1 \color{red}{ -6x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11+6x } & = & -1 \color{red}{ -6x }\color{blue}{-11+6x } \\\Leftrightarrow & -x \color{blue}{+6x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &5x & = &-12\\\Leftrightarrow & \color{red}{5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-13}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13-9x } & = & -12 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-5}& = & -8 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{-5}\color{blue}{+5+5x } & = & -8 \color{red}{ -5x }\color{blue}{+5+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & -8 \color{blue}{+5} \\\Leftrightarrow &6x & = &-3\\\Leftrightarrow & \color{red}{6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-5}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-x } & = & -6 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -6 \color{blue}{+5} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-11}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-x } & = & -9 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -9 \color{blue}{+11} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-15}& = & 3 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15+2x } & = & 3 \color{red}{ -2x }\color{blue}{+15+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & 3 \color{blue}{+15} \\\Leftrightarrow &11x & = &18\\\Leftrightarrow & \color{red}{11}x & = &18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+12}& = & -13 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12+10x } & = & -13 \color{red}{ -10x }\color{blue}{-12+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -13 \color{blue}{-12} \\\Leftrightarrow &21x & = &-25\\\Leftrightarrow & \color{red}{21}x & = &-25\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-25}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{21} } & & \\ & V = \left\{ \frac{-25}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-10}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-10}\color{blue}{+10-13x } & = & -9 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &-17x & = &1\\\Leftrightarrow & \color{red}{-17}x & = &1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+10}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+10}\color{blue}{-10-x } & = & 7 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &-14x & = &-3\\\Leftrightarrow & \color{red}{-14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)