Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+15}& = & 5 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15+12x } & = & 5 \color{red}{ -12x }\color{blue}{-15+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &25x & = &-10\\\Leftrightarrow & \color{red}{25}x & = &-10\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-10}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+12}& = & -13 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12+5x } & = & -13 \color{red}{ -5x }\color{blue}{-12+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & -13 \color{blue}{-12} \\\Leftrightarrow &13x & = &-25\\\Leftrightarrow & \color{red}{13}x & = &-25\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-25}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{13} } & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+15}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-x } & = & 14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-12}& = & 14 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12+2x } & = & 14 \color{red}{ -2x }\color{blue}{+12+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & 14 \color{blue}{+12} \\\Leftrightarrow &11x & = &26\\\Leftrightarrow & \color{red}{11}x & = &26\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{26}{11} \\\Leftrightarrow & \color{green}{ x = \frac{26}{11} } & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+6}& = & 7 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6+7x } & = & 7 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & -x \color{blue}{+7x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &6x & = &1\\\Leftrightarrow & \color{red}{6}x & = &1\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{1}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+8}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+8}\color{blue}{-8-x } & = & 13 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 13 \color{blue}{-8} \\\Leftrightarrow &-6x & = &5\\\Leftrightarrow & \color{red}{-6}x & = &5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-3}& = & -5 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3+12x } & = & -5 \color{red}{ -12x }\color{blue}{+3+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &17x & = &-2\\\Leftrightarrow & \color{red}{17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-8}& = & -5 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-8x } & = & -5 \color{red}{ +8x }\color{blue}{+8-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+4}& = & -12 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4+13x } & = & -12 \color{red}{ -13x }\color{blue}{-4+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -12 \color{blue}{-4} \\\Leftrightarrow &27x & = &-16\\\Leftrightarrow & \color{red}{27}x & = &-16\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-16}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{27} } & & \\ & V = \left\{ \frac{-16}{27} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-12}& = & -9 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+8x } & = & -9 \color{red}{ -8x }\color{blue}{+12+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -9 \color{blue}{+12} \\\Leftrightarrow &11x & = &3\\\Leftrightarrow & \color{red}{11}x & = &3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+8}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-x } & = & 3 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 3 \color{blue}{-8} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8-x } & = & 4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &-4x & = &12\\\Leftrightarrow & \color{red}{-4}x & = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)