Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+10}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-7x } & = & -3 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &-16x & = &-13\\\Leftrightarrow & \color{red}{-16}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-13}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{13}{16} } & & \\ & V = \left\{ \frac{13}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-1}& = & 9 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-1}\color{blue}{+1-14x } & = & 9 \color{red}{ +14x }\color{blue}{+1-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &-23x & = &10\\\Leftrightarrow & \color{red}{-23}x & = &10\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{10}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{23} } & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-x } & = & 4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-13}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13-x } & = & 3 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 3 \color{blue}{+13} \\\Leftrightarrow &-16x & = &16\\\Leftrightarrow & \color{red}{-16}x & = &16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{16}{-16} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-6}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x } & = & -12 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+8}& = & 12 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8+9x } & = & 12 \color{red}{ -9x }\color{blue}{-8+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 12 \color{blue}{-8} \\\Leftrightarrow &19x & = &4\\\Leftrightarrow & \color{red}{19}x & = &4\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{4}{19} \\\Leftrightarrow & \color{green}{ x = \frac{4}{19} } & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-5}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-5}\color{blue}{+5-x } & = & -3 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -3 \color{blue}{+5} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-5}& = & -8 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5+5x } & = & -8 \color{red}{ -5x }\color{blue}{+5+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & -8 \color{blue}{+5} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+2}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-7x } & = & -1 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -1 \color{blue}{-2} \\\Leftrightarrow &-13x & = &-3\\\Leftrightarrow & \color{red}{-13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+1}\color{blue}{-1-x } & = & 2 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 2 \color{blue}{-1} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+2}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2-13x } & = & -11 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -11 \color{blue}{-2} \\\Leftrightarrow &-28x & = &-13\\\Leftrightarrow & \color{red}{-28}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-13}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{13}{28} } & & \\ & V = \left\{ \frac{13}{28} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+15}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-9x } & = & -8 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & 13x \color{blue}{-9x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &4x & = &-23\\\Leftrightarrow & \color{red}{4}x & = &-23\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-23}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{4} } & & \\ & V = \left\{ \frac{-23}{4} \right\} & \\\end{align}\)