Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-6}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6+11x } & = & 2 \color{red}{ -11x }\color{blue}{+6+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 2 \color{blue}{+6} \\\Leftrightarrow &23x & = &8\\\Leftrightarrow & \color{red}{23}x & = &8\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{8}{23} \\\Leftrightarrow & \color{green}{ x = \frac{8}{23} } & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+6}& = & -1 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6+2x } & = & -1 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &5x & = &-7\\\Leftrightarrow & \color{red}{5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x } & = & 7 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 7 \color{blue}{-12} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-7}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7-x } & = & 15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &13x & = &22\\\Leftrightarrow & \color{red}{13}x & = &22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+3}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3-5x } & = & -2 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -2 \color{blue}{-3} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-11}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-x } & = & -1 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &-7x & = &10\\\Leftrightarrow & \color{red}{-7}x & = &10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-3}& = & 10 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-14x } & = & 10 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &-23x & = &13\\\Leftrightarrow & \color{red}{-23}x & = &13\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{13}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{23} } & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+1}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1-3x } & = & -2 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+8}& = & 7 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8+12x } & = & 7 \color{red}{ -12x }\color{blue}{-8+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 7 \color{blue}{-8} \\\Leftrightarrow &17x & = &-1\\\Leftrightarrow & \color{red}{17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+14}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14-9x } & = & 3 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &-20x & = &-11\\\Leftrightarrow & \color{red}{-20}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-11}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{11}{20} } & & \\ & V = \left\{ \frac{11}{20} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+10}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-x } & = & -3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &-12x & = &-13\\\Leftrightarrow & \color{red}{-12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-2}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-7x } & = & -12 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -12 \color{blue}{+2} \\\Leftrightarrow &-17x & = &-10\\\Leftrightarrow & \color{red}{-17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)