Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-13}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13+13x } & = & -13 \color{red}{ -13x }\color{blue}{+13+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -13 \color{blue}{+13} \\\Leftrightarrow &27x & = &0\\\Leftrightarrow & \color{red}{27}x & = &0\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{0}{27} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-5}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5-7x } & = & -4 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -4 \color{blue}{+5} \\\Leftrightarrow &-20x & = &1\\\Leftrightarrow & \color{red}{-20}x & = &1\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{1}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{20} } & & \\ & V = \left\{ \frac{-1}{20} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-9}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-13x } & = & -8 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-12}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-12}\color{blue}{+12+13x } & = & -3 \color{red}{ -13x }\color{blue}{+12+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -3 \color{blue}{+12} \\\Leftrightarrow &23x & = &9\\\Leftrightarrow & \color{red}{23}x & = &9\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{9}{23} \\\Leftrightarrow & \color{green}{ x = \frac{9}{23} } & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+10}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-3x } & = & 10 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 10 \color{blue}{-10} \\\Leftrightarrow &-8x & = &0\\\Leftrightarrow & \color{red}{-8}x & = &0\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{0}{-8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+10}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+10}\color{blue}{-10-x } & = & 7 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+4}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4-5x } & = & -1 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & -1 \color{blue}{-4} \\\Leftrightarrow &8x & = &-5\\\Leftrightarrow & \color{red}{8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+3}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3-x } & = & 12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &12x & = &9\\\Leftrightarrow & \color{red}{12}x & = &9\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{9}{12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-13}& = & 12 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-13}\color{blue}{+13+10x } & = & 12 \color{red}{ -10x }\color{blue}{+13+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &17x & = &25\\\Leftrightarrow & \color{red}{17}x & = &25\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{25}{17} \\\Leftrightarrow & \color{green}{ x = \frac{25}{17} } & & \\ & V = \left\{ \frac{25}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+15}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-7x } & = & 7 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & 7 \color{blue}{-15} \\\Leftrightarrow &-16x & = &-8\\\Leftrightarrow & \color{red}{-16}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+12}& = & -1 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12-6x } & = & -1 \color{red}{ +6x }\color{blue}{-12-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & -1 \color{blue}{-12} \\\Leftrightarrow &-x & = &-13\\\Leftrightarrow & \color{red}{-}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-13}{-1} \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-11}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-x } & = & 11 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 11 \color{blue}{+11} \\\Leftrightarrow &-7x & = &22\\\Leftrightarrow & \color{red}{-7}x & = &22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)