Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{-13}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13-x } & = & 6 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 6 \color{blue}{+13} \\\Leftrightarrow &-15x & = &19\\\Leftrightarrow & \color{red}{-15}x & = &19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{15} } & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-11}& = & -11 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-8x } & = & -11 \color{red}{ +8x }\color{blue}{+11-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -11 \color{blue}{+11} \\\Leftrightarrow &-23x & = &0\\\Leftrightarrow & \color{red}{-23}x & = &0\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{0}{-23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-10}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10-x } & = & 9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 9 \color{blue}{+10} \\\Leftrightarrow &-7x & = &19\\\Leftrightarrow & \color{red}{-7}x & = &19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+13}& = & 14 \color{red}{ +4x } \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13-4x } & = & 14 \color{red}{ +4x }\color{blue}{-13-4x } \\\Leftrightarrow & -11x \color{blue}{-4x } & = & 14 \color{blue}{-13} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+7}& = & -11 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+7}\color{blue}{-7-4x } & = & -11 \color{red}{ +4x }\color{blue}{-7-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &-7x & = &-18\\\Leftrightarrow & \color{red}{-7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+6}& = & 9 \color{red}{ +2x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6-2x } & = & 9 \color{red}{ +2x }\color{blue}{-6-2x } \\\Leftrightarrow & x \color{blue}{-2x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-x } & = & 1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &-15x & = &-9\\\Leftrightarrow & \color{red}{-15}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-4}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4-13x } & = & 15 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & 15 \color{blue}{+4} \\\Leftrightarrow &2x & = &19\\\Leftrightarrow & \color{red}{2}x & = &19\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{19}{2} \\\Leftrightarrow & \color{green}{ x = \frac{19}{2} } & & \\ & V = \left\{ \frac{19}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+11}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-3x } & = & -11 \color{red}{ +3x }\color{blue}{-11-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -11 \color{blue}{-11} \\\Leftrightarrow &-5x & = &-22\\\Leftrightarrow & \color{red}{-5}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-7}& = & -6 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7-4x } & = & -6 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & -6 \color{blue}{+7} \\\Leftrightarrow &9x & = &1\\\Leftrightarrow & \color{red}{9}x & = &1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8-x } & = & 4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &-4x & = &12\\\Leftrightarrow & \color{red}{-4}x & = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+15}& = & 14 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-14x } & = & 14 \color{red}{ +14x }\color{blue}{-15-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &-23x & = &-1\\\Leftrightarrow & \color{red}{-23}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-1}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{1}{23} } & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)