Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-12}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+11x } & = & 9 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &14x & = &21\\\Leftrightarrow & \color{red}{14}x & = &21\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{21}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-5}& = & -2 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5+9x } & = & -2 \color{red}{ -9x }\color{blue}{+5+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & -2 \color{blue}{+5} \\\Leftrightarrow &8x & = &3\\\Leftrightarrow & \color{red}{8}x & = &3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-10}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10-x } & = & 8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 8 \color{blue}{+10} \\\Leftrightarrow &11x & = &18\\\Leftrightarrow & \color{red}{11}x & = &18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-2}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2-5x } & = & 2 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 2 \color{blue}{+2} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-11}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11-7x } & = & 4 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -x \color{blue}{-7x } & = & 4 \color{blue}{+11} \\\Leftrightarrow &-8x & = &15\\\Leftrightarrow & \color{red}{-8}x & = &15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-7}& = & -7 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7-11x } & = & -7 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+8}& = & -11 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8-12x } & = & -11 \color{red}{ +12x }\color{blue}{-8-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &-5x & = &-19\\\Leftrightarrow & \color{red}{-5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-1}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1-13x } & = & -10 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -10 \color{blue}{+1} \\\Leftrightarrow &-x & = &-9\\\Leftrightarrow & \color{red}{-}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-9}{-1} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+4}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & 3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &-14x & = &-1\\\Leftrightarrow & \color{red}{-14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-9}& = & -11 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-14x } & = & -11 \color{red}{ +14x }\color{blue}{+9-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &-23x & = &-2\\\Leftrightarrow & \color{red}{-23}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-2}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{2}{23} } & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-5}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-3x } & = & 14 \color{red}{ +3x }\color{blue}{+5-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &-x & = &19\\\Leftrightarrow & \color{red}{-}x & = &19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{19}{-1} \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4-x } & = & -14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &5x & = &-18\\\Leftrightarrow & \color{red}{5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)