Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(x-4=14+0x\)
2. \(9x-8=-7+10x\)
3. \(-2x+8=-8+5x\)
4. \(15x-12=14-2x\)
5. \(7x-2=8-2x\)
6. \(-6x-12=-4+13x\)
7. \(-5x+13=1+3x\)
8. \(11x-6=-15-13x\)
9. \(x+11=8-8x\)
10. \(-9x-11=-2+14x\)
11. \(7x-6=-13-3x\)
12. \(11x-7=-7-2x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-4}& = & 14 \color{red}{ +0x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4+0x } & = & 14 \color{red}{ +0x }\color{blue}{+4+0x } \\\Leftrightarrow & x \color{blue}{+0x } & = & 14 \color{blue}{+4} \\\Leftrightarrow &x & = &18\\\Leftrightarrow & \color{red}{}x & = &18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 18 \\\Leftrightarrow & \color{green}{ x = 18 } & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-8}& = & -7 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8-10x } & = & -7 \color{red}{ +10x }\color{blue}{+8-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -7 \color{blue}{+8} \\\Leftrightarrow &-x & = &1\\\Leftrightarrow & \color{red}{-}x & = &1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{1}{-1} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+8}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-5x } & = & -8 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &-7x & = &-16\\\Leftrightarrow & \color{red}{-7}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-12}& = & 14 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12+2x } & = & 14 \color{red}{ -2x }\color{blue}{+12+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 14 \color{blue}{+12} \\\Leftrightarrow &17x & = &26\\\Leftrightarrow & \color{red}{17}x & = &26\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{26}{17} \\\Leftrightarrow & \color{green}{ x = \frac{26}{17} } & & \\ & V = \left\{ \frac{26}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-2}& = & 8 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2+2x } & = & 8 \color{red}{ -2x }\color{blue}{+2+2x } \\\Leftrightarrow & 7x \color{blue}{+2x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &9x & = &10\\\Leftrightarrow & \color{red}{9}x & = &10\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{10}{9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-12}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-13x } & = & -4 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &-19x & = &8\\\Leftrightarrow & \color{red}{-19}x & = &8\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{8}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+13}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-3x } & = & 1 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 1 \color{blue}{-13} \\\Leftrightarrow &-8x & = &-12\\\Leftrightarrow & \color{red}{-8}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-6}& = & -15 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6+13x } & = & -15 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &24x & = &-9\\\Leftrightarrow & \color{red}{24}x & = &-9\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-9}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+11}& = & 8 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{+11}\color{blue}{-11+8x } & = & 8 \color{red}{ -8x }\color{blue}{-11+8x } \\\Leftrightarrow & x \color{blue}{+8x } & = & 8 \color{blue}{-11} \\\Leftrightarrow &9x & = &-3\\\Leftrightarrow & \color{red}{9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-11}& = & -2 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-14x } & = & -2 \color{red}{ +14x }\color{blue}{+11-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -2 \color{blue}{+11} \\\Leftrightarrow &-23x & = &9\\\Leftrightarrow & \color{red}{-23}x & = &9\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{9}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{23} } & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-6}& = & -13 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6+3x } & = & -13 \color{red}{ -3x }\color{blue}{+6+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -13 \color{blue}{+6} \\\Leftrightarrow &10x & = &-7\\\Leftrightarrow & \color{red}{10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-7}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-7}& = & -7 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7+2x } & = & -7 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &13x & = &0\\\Leftrightarrow & \color{red}{13}x & = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)