Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-5}& = & -4 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-4x } & = & -4 \color{red}{ +4x }\color{blue}{+5-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -4 \color{blue}{+5} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-3}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-13x } & = & -6 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -6 \color{blue}{+3} \\\Leftrightarrow &-25x & = &-3\\\Leftrightarrow & \color{red}{-25}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-3}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{3}{25} } & & \\ & V = \left\{ \frac{3}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+12}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12-14x } & = & -7 \color{red}{ +14x }\color{blue}{-12-14x } \\\Leftrightarrow & 3x \color{blue}{-14x } & = & -7 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-19\\\Leftrightarrow & \color{red}{-11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-19}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-5}& = & 14 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5+11x } & = & 14 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &14x & = &19\\\Leftrightarrow & \color{red}{14}x & = &19\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{19}{14} \\\Leftrightarrow & \color{green}{ x = \frac{19}{14} } & & \\ & V = \left\{ \frac{19}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-12}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-x } & = & -6 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -6 \color{blue}{+12} \\\Leftrightarrow &-7x & = &6\\\Leftrightarrow & \color{red}{-7}x & = &6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+15}& = & -11 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15+2x } & = & -11 \color{red}{ -2x }\color{blue}{-15+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &7x & = &-26\\\Leftrightarrow & \color{red}{7}x & = &-26\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-26}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{7} } & & \\ & V = \left\{ \frac{-26}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+1}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x } & = & 7 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 7 \color{blue}{-1} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{-2}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2-x } & = & 7 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &-4x & = &9\\\Leftrightarrow & \color{red}{-4}x & = &9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-14}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-x } & = & 10 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 10 \color{blue}{+14} \\\Leftrightarrow &x & = &24\\\Leftrightarrow & \color{red}{}x & = &24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 24 \\\Leftrightarrow & \color{green}{ x = 24 } & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+1}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1-5x } & = & -15 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & -15 \color{blue}{-1} \\\Leftrightarrow &-x & = &-16\\\Leftrightarrow & \color{red}{-}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-16}{-1} \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{-11}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11-7x } & = & -1 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &5x & = &10\\\Leftrightarrow & \color{red}{5}x & = &10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{10}{5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-9}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-x } & = & -6 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &-4x & = &3\\\Leftrightarrow & \color{red}{-4}x & = &3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)