Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+4}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-7x } & = & -14 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-20x & = &-18\\\Leftrightarrow & \color{red}{-20}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-18}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8-x } & = & -8 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -8 \color{blue}{+8} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+5}& = & 3 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5+10x } & = & 3 \color{red}{ -10x }\color{blue}{-5+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &17x & = &-2\\\Leftrightarrow & \color{red}{17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-8}& = & -4 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8+12x } & = & -4 \color{red}{ -12x }\color{blue}{+8+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &17x & = &4\\\Leftrightarrow & \color{red}{17}x & = &4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+13}& = & 4 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13+8x } & = & 4 \color{red}{ -8x }\color{blue}{-13+8x } \\\Leftrightarrow & -x \color{blue}{+8x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &7x & = &-9\\\Leftrightarrow & \color{red}{7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+9}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9-x } & = & -3 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -3 \color{blue}{-9} \\\Leftrightarrow &-15x & = &-12\\\Leftrightarrow & \color{red}{-15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-3}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3-x } & = & -9 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &13x & = &-6\\\Leftrightarrow & \color{red}{13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-3}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3-7x } & = & -2 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+15}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-7x } & = & -3 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -3 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-18\\\Leftrightarrow & \color{red}{-5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-6}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-4x } & = & -8 \color{red}{ +4x }\color{blue}{+6-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -8 \color{blue}{+6} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-8}\color{blue}{+8-x } & = & 4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-x } & = & -15 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &-10x & = &-5\\\Leftrightarrow & \color{red}{-10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)