Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+6}& = & -2 \color{red}{ +2x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6-2x } & = & -2 \color{red}{ +2x }\color{blue}{-6-2x } \\\Leftrightarrow & x \color{blue}{-2x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &-x & = &-8\\\Leftrightarrow & \color{red}{-}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-8}{-1} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+13}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13-11x } & = & 11 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &-5x & = &-2\\\Leftrightarrow & \color{red}{-5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11-x } & = & -14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-6}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6-13x } & = & 13 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &-8x & = &19\\\Leftrightarrow & \color{red}{-8}x & = &19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-12}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12-7x } & = & 3 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &-3x & = &15\\\Leftrightarrow & \color{red}{-3}x & = &15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{15}{-3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+5}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5-x } & = & -15 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &-5x & = &-20\\\Leftrightarrow & \color{red}{-5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-20}{-5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-1}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1+11x } & = & 10 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & x \color{blue}{+11x } & = & 10 \color{blue}{+1} \\\Leftrightarrow &12x & = &11\\\Leftrightarrow & \color{red}{12}x & = &11\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{11}{12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{12} } & & \\ & V = \left\{ \frac{11}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-1}& = & 15 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1+15x } & = & 15 \color{red}{ -15x }\color{blue}{+1+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &14x & = &16\\\Leftrightarrow & \color{red}{14}x & = &16\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{16}{14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-x } & = & -2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &-10x & = &6\\\Leftrightarrow & \color{red}{-10}x & = &6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+11}& = & 12 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11+7x } & = & 12 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &15x & = &1\\\Leftrightarrow & \color{red}{15}x & = &1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-x } & = & 13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &-15x & = &22\\\Leftrightarrow & \color{red}{-15}x & = &22\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{22}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{15} } & & \\ & V = \left\{ \frac{-22}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-12}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12-x } & = & 8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 8 \color{blue}{+12} \\\Leftrightarrow &7x & = &20\\\Leftrightarrow & \color{red}{7}x & = &20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{20}{7} } & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)