Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+5}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5-11x } & = & 4 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-x } & = & 11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &-14x & = &17\\\Leftrightarrow & \color{red}{-14}x & = &17\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{17}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{14} } & & \\ & V = \left\{ \frac{-17}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+3}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-7x } & = & 4 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+6}& = & 13 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6+10x } & = & 13 \color{red}{ -10x }\color{blue}{-6+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 13 \color{blue}{-6} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-5}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-5}\color{blue}{+5-7x } & = & -4 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & -4 \color{blue}{+5} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-5}\color{blue}{+5-x } & = & -9 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &13x & = &-4\\\Leftrightarrow & \color{red}{13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-5}& = & -12 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-10x } & = & -12 \color{red}{ +10x }\color{blue}{+5-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -12 \color{blue}{+5} \\\Leftrightarrow &-19x & = &-7\\\Leftrightarrow & \color{red}{-19}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-7}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+5}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5-11x } & = & 3 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+15}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-5x } & = & -12 \color{red}{ +5x }\color{blue}{-15-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &-17x & = &-27\\\Leftrightarrow & \color{red}{-17}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-27}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{27}{17} } & & \\ & V = \left\{ \frac{27}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+4}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4+11x } & = & -7 \color{red}{ -11x }\color{blue}{-4+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &23x & = &-11\\\Leftrightarrow & \color{red}{23}x & = &-11\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-11}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{23} } & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-4}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4+13x } & = & -14 \color{red}{ -13x }\color{blue}{+4+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &12x & = &-10\\\Leftrightarrow & \color{red}{12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-10}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+13}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+13}\color{blue}{-13-5x } & = & 15 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)