Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+11}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11-x } & = & 8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 8 \color{blue}{-11} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-5}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5-5x } & = & -4 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -4 \color{blue}{+5} \\\Leftrightarrow &7x & = &1\\\Leftrightarrow & \color{red}{7}x & = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+4}& = & 12 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4+15x } & = & 12 \color{red}{ -15x }\color{blue}{-4+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &23x & = &8\\\Leftrightarrow & \color{red}{23}x & = &8\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{8}{23} \\\Leftrightarrow & \color{green}{ x = \frac{8}{23} } & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+5}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & -3 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &-12x & = &-8\\\Leftrightarrow & \color{red}{-12}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-3}\color{blue}{+3-x } & = & 13 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 13 \color{blue}{+3} \\\Leftrightarrow &-3x & = &16\\\Leftrightarrow & \color{red}{-3}x & = &16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+6}& = & 14 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6+11x } & = & 14 \color{red}{ -11x }\color{blue}{-6+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 14 \color{blue}{-6} \\\Leftrightarrow &25x & = &8\\\Leftrightarrow & \color{red}{25}x & = &8\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{8}{25} \\\Leftrightarrow & \color{green}{ x = \frac{8}{25} } & & \\ & V = \left\{ \frac{8}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+12}& = & 8 \color{red}{ -6x } \\\Leftrightarrow & x \color{red}{+12}\color{blue}{-12+6x } & = & 8 \color{red}{ -6x }\color{blue}{-12+6x } \\\Leftrightarrow & x \color{blue}{+6x } & = & 8 \color{blue}{-12} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-8}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-5x } & = & 1 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &-9x & = &9\\\Leftrightarrow & \color{red}{-9}x & = &9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{9}{-9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+3}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-5x } & = & -11 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -11 \color{blue}{-3} \\\Leftrightarrow &-14x & = &-14\\\Leftrightarrow & \color{red}{-14}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-14}{-14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-8x & = &0\\\Leftrightarrow & \color{red}{-8}x & = &0\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{0}{-8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+4}& = & -7 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4+3x } & = & -7 \color{red}{ -3x }\color{blue}{-4+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &10x & = &-11\\\Leftrightarrow & \color{red}{10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-5}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-x } & = & -12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -12 \color{blue}{+5} \\\Leftrightarrow &-8x & = &-7\\\Leftrightarrow & \color{red}{-8}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)