Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-7}& = & 15 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7-6x } & = & 15 \color{red}{ +6x }\color{blue}{+7-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &-17x & = &22\\\Leftrightarrow & \color{red}{-17}x & = &22\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{22}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{17} } & & \\ & V = \left\{ \frac{-22}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+8}& = & -2 \color{red}{ -14x } \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8+14x } & = & -2 \color{red}{ -14x }\color{blue}{-8+14x } \\\Leftrightarrow & -x \color{blue}{+14x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &13x & = &-10\\\Leftrightarrow & \color{red}{13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-5}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5-13x } & = & -4 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -4 \color{blue}{+5} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+7}& = & -1 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{+7}\color{blue}{-7-10x } & = & -1 \color{red}{ +10x }\color{blue}{-7-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &-7x & = &-8\\\Leftrightarrow & \color{red}{-7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+1}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1-7x } & = & -3 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -3 \color{blue}{-1} \\\Leftrightarrow &-5x & = &-4\\\Leftrightarrow & \color{red}{-5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-2}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2-x } & = & 8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &-4x & = &10\\\Leftrightarrow & \color{red}{-4}x & = &10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+2}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-14x } & = & -7 \color{red}{ +14x }\color{blue}{-2-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -7 \color{blue}{-2} \\\Leftrightarrow &-23x & = &-9\\\Leftrightarrow & \color{red}{-23}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-9}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{9}{23} } & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+4}& = & -14 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4-12x } & = & -14 \color{red}{ +12x }\color{blue}{-4-12x } \\\Leftrightarrow & 5x \color{blue}{-12x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-7x & = &-18\\\Leftrightarrow & \color{red}{-7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-8}& = & -12 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8+14x } & = & -12 \color{red}{ -14x }\color{blue}{+8+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -12 \color{blue}{+8} \\\Leftrightarrow &19x & = &-4\\\Leftrightarrow & \color{red}{19}x & = &-4\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-4}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-x } & = & 9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 9 \color{blue}{-1} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+15}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-x } & = & -1 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-16\\\Leftrightarrow & \color{red}{-5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-6}& = & -1 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6+12x } & = & -1 \color{red}{ -12x }\color{blue}{+6+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -1 \color{blue}{+6} \\\Leftrightarrow &25x & = &5\\\Leftrightarrow & \color{red}{25}x & = &5\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{5}{25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)