Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+13}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-x } & = & -8 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -8 \color{blue}{-13} \\\Leftrightarrow &-8x & = &-21\\\Leftrightarrow & \color{red}{-8}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-21}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{21}{8} } & & \\ & V = \left\{ \frac{21}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-13}\color{blue}{+13-x } & = & -11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &6x & = &2\\\Leftrightarrow & \color{red}{6}x & = &2\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{2}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-15}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15-x } & = & -5 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -5 \color{blue}{+15} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+9}& = & 5 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+9}\color{blue}{-9-4x } & = & 5 \color{red}{ +4x }\color{blue}{-9-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 5 \color{blue}{-9} \\\Leftrightarrow &-7x & = &-4\\\Leftrightarrow & \color{red}{-7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-12}& = & 5 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12+11x } & = & 5 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &25x & = &17\\\Leftrightarrow & \color{red}{25}x & = &17\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{17}{25} \\\Leftrightarrow & \color{green}{ x = \frac{17}{25} } & & \\ & V = \left\{ \frac{17}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+14}& = & 8 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14+8x } & = & 8 \color{red}{ -8x }\color{blue}{-14+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 8 \color{blue}{-14} \\\Leftrightarrow &19x & = &-6\\\Leftrightarrow & \color{red}{19}x & = &-6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{19} } & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13-x } & = & 4 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{+13} \\\Leftrightarrow &-3x & = &17\\\Leftrightarrow & \color{red}{-3}x & = &17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{3} } & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-4}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4-11x } & = & -3 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &-18x & = &1\\\Leftrightarrow & \color{red}{-18}x & = &1\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{1}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{18} } & & \\ & V = \left\{ \frac{-1}{18} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-7}& = & 3 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7-4x } & = & 3 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & 3 \color{blue}{+7} \\\Leftrightarrow &x & = &10\\\Leftrightarrow & \color{red}{}x & = &10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 10 \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+4}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-13x } & = & -6 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &-19x & = &-10\\\Leftrightarrow & \color{red}{-19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-10}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-15}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15-x } & = & 4 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 4 \color{blue}{+15} \\\Leftrightarrow &-4x & = &19\\\Leftrightarrow & \color{red}{-4}x & = &19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{4} } & & \\ & V = \left\{ \frac{-19}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-13}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13-13x } & = & 12 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &-17x & = &25\\\Leftrightarrow & \color{red}{-17}x & = &25\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{25}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{17} } & & \\ & V = \left\{ \frac{-25}{17} \right\} & \\\end{align}\)