Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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