Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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