Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+3}& = & -3 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3+12x } & = & -3 \color{red}{ -12x }\color{blue}{-3+12x } \\\Leftrightarrow & -x \color{blue}{+12x } & = & -3 \color{blue}{-3} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-2}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-2}\color{blue}{+2-x } & = & -1 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -1 \color{blue}{+2} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-6}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6-11x } & = & 1 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+4}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4-x } & = & 11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 11 \color{blue}{-4} \\\Leftrightarrow &10x & = &7\\\Leftrightarrow & \color{red}{10}x & = &7\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{7}{10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+3}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3-x } & = & -8 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -8 \color{blue}{-3} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+7}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-5x } & = & 8 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 8 \color{blue}{-7} \\\Leftrightarrow &-19x & = &1\\\Leftrightarrow & \color{red}{-19}x & = &1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-9}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-x } & = & 11 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 11 \color{blue}{+9} \\\Leftrightarrow &-7x & = &20\\\Leftrightarrow & \color{red}{-7}x & = &20\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{20}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{7} } & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-13}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-x } & = & 12 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &-9x & = &25\\\Leftrightarrow & \color{red}{-9}x & = &25\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{25}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{9} } & & \\ & V = \left\{ \frac{-25}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+1}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1-7x } & = & 8 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & 8 \color{blue}{-1} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-5}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5-7x } & = & -13 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+11}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-x } & = & -9 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -9 \color{blue}{-11} \\\Leftrightarrow &-9x & = &-20\\\Leftrightarrow & \color{red}{-9}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{20}{9} } & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-2}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{-2}\color{blue}{+2-5x } & = & -5 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)