Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+13}& = & -3 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13-9x } & = & -3 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -3 \color{blue}{-13} \\\Leftrightarrow &5x & = &-16\\\Leftrightarrow & \color{red}{5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+12}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12-x } & = & -14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -14 \color{blue}{-12} \\\Leftrightarrow &-14x & = &-26\\\Leftrightarrow & \color{red}{-14}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-26}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+4}& = & -15 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4+7x } & = & -15 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &22x & = &-19\\\Leftrightarrow & \color{red}{22}x & = &-19\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-19}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{22} } & & \\ & V = \left\{ \frac{-19}{22} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+13}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13-7x } & = & 12 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 12 \color{blue}{-13} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-13}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-3x } & = & 1 \color{red}{ +3x }\color{blue}{+13-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 1 \color{blue}{+13} \\\Leftrightarrow &-x & = &14\\\Leftrightarrow & \color{red}{-}x & = &14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{14}{-1} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-10}& = & -6 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10-9x } & = & -6 \color{red}{ +9x }\color{blue}{+10-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -6 \color{blue}{+10} \\\Leftrightarrow &5x & = &4\\\Leftrightarrow & \color{red}{5}x & = &4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+6}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-x } & = & 8 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-11}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-x } & = & -1 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &-15x & = &10\\\Leftrightarrow & \color{red}{-15}x & = &10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & 5 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-12}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12-x } & = & 6 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 6 \color{blue}{+12} \\\Leftrightarrow &5x & = &18\\\Leftrightarrow & \color{red}{5}x & = &18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-7}& = & 11 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7+12x } & = & 11 \color{red}{ -12x }\color{blue}{+7+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 11 \color{blue}{+7} \\\Leftrightarrow &25x & = &18\\\Leftrightarrow & \color{red}{25}x & = &18\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{18}{25} \\\Leftrightarrow & \color{green}{ x = \frac{18}{25} } & & \\ & V = \left\{ \frac{18}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-14}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14-13x } & = & 9 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 9 \color{blue}{+14} \\\Leftrightarrow &-19x & = &23\\\Leftrightarrow & \color{red}{-19}x & = &23\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{23}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{19} } & & \\ & V = \left\{ \frac{-23}{19} \right\} & \\\end{align}\)