Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+12}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-9x } & = & 5 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+14}& = & -6 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-3x } & = & -6 \color{red}{ +3x }\color{blue}{-14-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-20\\\Leftrightarrow & \color{red}{-5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-20}{-5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-1}& = & -2 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1+12x } & = & -2 \color{red}{ -12x }\color{blue}{+1+12x } \\\Leftrightarrow & -x \color{blue}{+12x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-9}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9-7x } & = & -14 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & 11x \color{blue}{-7x } & = & -14 \color{blue}{+9} \\\Leftrightarrow &4x & = &-5\\\Leftrightarrow & \color{red}{4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-5}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-2}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2-3x } & = & 3 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & 3 \color{blue}{+2} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+6}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6+11x } & = & -9 \color{red}{ -11x }\color{blue}{-6+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &17x & = &-15\\\Leftrightarrow & \color{red}{17}x & = &-15\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-15}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{17} } & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-12}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12-13x } & = & -4 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &-x & = &8\\\Leftrightarrow & \color{red}{-}x & = &8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{8}{-1} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-8}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-8}\color{blue}{+8-11x } & = & -12 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -12 \color{blue}{+8} \\\Leftrightarrow &-21x & = &-4\\\Leftrightarrow & \color{red}{-21}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-4}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{4}{21} } & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+2}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & -9 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -9 \color{blue}{-2} \\\Leftrightarrow &-4x & = &-11\\\Leftrightarrow & \color{red}{-4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+12}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-9x } & = & -4 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & -4 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-16\\\Leftrightarrow & \color{red}{-11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+11}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11+11x } & = & 1 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 1 \color{blue}{-11} \\\Leftrightarrow &23x & = &-10\\\Leftrightarrow & \color{red}{23}x & = &-10\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-10}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{23} } & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-1}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1-5x } & = & 14 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & 14 \color{blue}{+1} \\\Leftrightarrow &-6x & = &15\\\Leftrightarrow & \color{red}{-6}x & = &15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)