Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-12}& = & 12 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12+11x } & = & 12 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &17x & = &24\\\Leftrightarrow & \color{red}{17}x & = &24\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{24}{17} \\\Leftrightarrow & \color{green}{ x = \frac{24}{17} } & & \\ & V = \left\{ \frac{24}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+10}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-x } & = & 6 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 6 \color{blue}{-10} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+4}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4-x } & = & -12 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -12 \color{blue}{-4} \\\Leftrightarrow &12x & = &-16\\\Leftrightarrow & \color{red}{12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-16}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+13}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{+13}\color{blue}{-13-5x } & = & -15 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & 7x \color{blue}{-5x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &2x & = &-28\\\Leftrightarrow & \color{red}{2}x & = &-28\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-28}{2} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+8}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8-5x } & = & -15 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & -15 \color{blue}{-8} \\\Leftrightarrow &-x & = &-23\\\Leftrightarrow & \color{red}{-}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-23}{-1} \\\Leftrightarrow & \color{green}{ x = 23 } & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+12}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12+7x } & = & -2 \color{red}{ -7x }\color{blue}{-12+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -2 \color{blue}{-12} \\\Leftrightarrow &11x & = &-14\\\Leftrightarrow & \color{red}{11}x & = &-14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-9}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9-11x } & = & 7 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &4x & = &16\\\Leftrightarrow & \color{red}{4}x & = &16\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{16}{4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+7}& = & -5 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7+6x } & = & -5 \color{red}{ -6x }\color{blue}{-7+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -5 \color{blue}{-7} \\\Leftrightarrow &19x & = &-12\\\Leftrightarrow & \color{red}{19}x & = &-12\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-12}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{19} } & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12-x } & = & 7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 7 \color{blue}{+12} \\\Leftrightarrow &5x & = &19\\\Leftrightarrow & \color{red}{5}x & = &19\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{19}{5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+5}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-13x } & = & -1 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &-16x & = &-6\\\Leftrightarrow & \color{red}{-16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+2}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & -12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -12 \color{blue}{-2} \\\Leftrightarrow &-4x & = &-14\\\Leftrightarrow & \color{red}{-4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-14}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+11}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11-7x } & = & 3 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &3x & = &-8\\\Leftrightarrow & \color{red}{3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)