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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(14x-6=-13+9x\)
2. \(-x-7=-6-9x\)
3. \(9x-5=-4+x\)
4. \(-2x+8=4+x\)
5. \(14x-12=-9-13x\)
6. \(-13x-12=8+x\)
7. \(15x-3=-3-7x\)
8. \(12x+7=-11+x\)
9. \(8x-8=-3+x\)
10. \(6x+6=-12-5x\)
11. \(8x+6=-2+11x\)
12. \(-8x+6=7+x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-6}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6-9x } & = & -13 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -13 \color{blue}{+6} \\\Leftrightarrow &5x & = &-7\\\Leftrightarrow & \color{red}{5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-7}& = & -6 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7+9x } & = & -6 \color{red}{ -9x }\color{blue}{+7+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & -6 \color{blue}{+7} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-5}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5-x } & = & -4 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -4 \color{blue}{+5} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-x } & = & 4 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-12}& = & -9 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12+13x } & = & -9 \color{red}{ -13x }\color{blue}{+12+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -9 \color{blue}{+12} \\\Leftrightarrow &27x & = &3\\\Leftrightarrow & \color{red}{27}x & = &3\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{3}{27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-12}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-x } & = & 8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 8 \color{blue}{+12} \\\Leftrightarrow &-14x & = &20\\\Leftrightarrow & \color{red}{-14}x & = &20\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{20}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-3}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-3}\color{blue}{+3+7x } & = & -3 \color{red}{ -7x }\color{blue}{+3+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -3 \color{blue}{+3} \\\Leftrightarrow &22x & = &0\\\Leftrightarrow & \color{red}{22}x & = &0\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{0}{22} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+7}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7-x } & = & -11 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &11x & = &-18\\\Leftrightarrow & \color{red}{11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-8}\color{blue}{+8-x } & = & -3 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &7x & = &5\\\Leftrightarrow & \color{red}{7}x & = &5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+6}& = & -12 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6+5x } & = & -12 \color{red}{ -5x }\color{blue}{-6+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &11x & = &-18\\\Leftrightarrow & \color{red}{11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+6}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6-11x } & = & -2 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-x } & = & 7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &-9x & = &1\\\Leftrightarrow & \color{red}{-9}x & = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)