Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+3}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3-x } & = & 2 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+11}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-x } & = & -7 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -7 \color{blue}{-11} \\\Leftrightarrow &-16x & = &-18\\\Leftrightarrow & \color{red}{-16}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-18}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-6}& = & -4 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-6}\color{blue}{+6+11x } & = & -4 \color{red}{ -11x }\color{blue}{+6+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &17x & = &2\\\Leftrightarrow & \color{red}{17}x & = &2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+13}& = & 13 \color{red}{ +6x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13-6x } & = & 13 \color{red}{ +6x }\color{blue}{-13-6x } \\\Leftrightarrow & -x \color{blue}{-6x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+4}& = & 13 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+4}\color{blue}{-4-6x } & = & 13 \color{red}{ +6x }\color{blue}{-4-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &-17x & = &9\\\Leftrightarrow & \color{red}{-17}x & = &9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{17} } & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+13}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13-x } & = & -5 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &-3x & = &-18\\\Leftrightarrow & \color{red}{-3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-18}{-3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-5}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5-x } & = & -10 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -10 \color{blue}{+5} \\\Leftrightarrow &7x & = &-5\\\Leftrightarrow & \color{red}{7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+12}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-3x } & = & -2 \color{red}{ +3x }\color{blue}{-12-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -2 \color{blue}{-12} \\\Leftrightarrow &-14x & = &-14\\\Leftrightarrow & \color{red}{-14}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-14}{-14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-6}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6-7x } & = & 14 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & 14 \color{blue}{+6} \\\Leftrightarrow &2x & = &20\\\Leftrightarrow & \color{red}{2}x & = &20\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{20}{2} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8-x } & = & -2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &-12x & = &6\\\Leftrightarrow & \color{red}{-12}x & = &6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-9}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-x } & = & -15 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -15 \color{blue}{+9} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-12}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12-13x } & = & 13 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &-8x & = &25\\\Leftrightarrow & \color{red}{-8}x & = &25\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{25}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{8} } & & \\ & V = \left\{ \frac{-25}{8} \right\} & \\\end{align}\)