Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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