Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+15}& = & -11 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-9x } & = & -11 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &-17x & = &-26\\\Leftrightarrow & \color{red}{-17}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-26}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{26}{17} } & & \\ & V = \left\{ \frac{26}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+6}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6+7x } & = & -13 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -13 \color{blue}{-6} \\\Leftrightarrow &11x & = &-19\\\Leftrightarrow & \color{red}{11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-19}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{11} } & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-9}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-13x } & = & 11 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 11 \color{blue}{+9} \\\Leftrightarrow &-19x & = &20\\\Leftrightarrow & \color{red}{-19}x & = &20\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{20}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{19} } & & \\ & V = \left\{ \frac{-20}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-1}& = & -8 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1-6x } & = & -8 \color{red}{ +6x }\color{blue}{+1-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & -8 \color{blue}{+1} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-14}& = & 1 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14+7x } & = & 1 \color{red}{ -7x }\color{blue}{+14+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 1 \color{blue}{+14} \\\Leftrightarrow &19x & = &15\\\Leftrightarrow & \color{red}{19}x & = &15\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{15}{19} \\\Leftrightarrow & \color{green}{ x = \frac{15}{19} } & & \\ & V = \left\{ \frac{15}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+7}& = & 15 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7+3x } & = & 15 \color{red}{ -3x }\color{blue}{-7+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 15 \color{blue}{-7} \\\Leftrightarrow &13x & = &8\\\Leftrightarrow & \color{red}{13}x & = &8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-13}& = & 3 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13+3x } & = & 3 \color{red}{ -3x }\color{blue}{+13+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 3 \color{blue}{+13} \\\Leftrightarrow &13x & = &16\\\Leftrightarrow & \color{red}{13}x & = &16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-2}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-13x } & = & 14 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 14 \color{blue}{+2} \\\Leftrightarrow &-19x & = &16\\\Leftrightarrow & \color{red}{-19}x & = &16\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{16}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{19} } & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-5}& = & 5 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5+2x } & = & 5 \color{red}{ -2x }\color{blue}{+5+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 5 \color{blue}{+5} \\\Leftrightarrow &13x & = &10\\\Leftrightarrow & \color{red}{13}x & = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-13}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-13}\color{blue}{+13-x } & = & 12 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &-6x & = &25\\\Leftrightarrow & \color{red}{-6}x & = &25\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{25}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{6} } & & \\ & V = \left\{ \frac{-25}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-11}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-x } & = & -12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+3}& = & 5 \color{red}{ +2x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3-2x } & = & 5 \color{red}{ +2x }\color{blue}{-3-2x } \\\Leftrightarrow & x \color{blue}{-2x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &-x & = &2\\\Leftrightarrow & \color{red}{-}x & = &2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{2}{-1} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)