Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-9}& = & -11 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9+5x } & = & -11 \color{red}{ -5x }\color{blue}{+9+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &16x & = &-2\\\Leftrightarrow & \color{red}{16}x & = &-2\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-2}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+9}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+9}\color{blue}{-9-13x } & = & 5 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & 5 \color{blue}{-9} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+4}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-13x } & = & -5 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &-28x & = &-9\\\Leftrightarrow & \color{red}{-28}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-9}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{9}{28} } & & \\ & V = \left\{ \frac{9}{28} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-15}& = & -6 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15-14x } & = & -6 \color{red}{ +14x }\color{blue}{+15-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+7}& = & -4 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{+7}\color{blue}{-7+14x } & = & -4 \color{red}{ -14x }\color{blue}{-7+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -4 \color{blue}{-7} \\\Leftrightarrow &17x & = &-11\\\Leftrightarrow & \color{red}{17}x & = &-11\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-11}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{17} } & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+1}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1-13x } & = & 3 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+13}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13-5x } & = & -7 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &-14x & = &-20\\\Leftrightarrow & \color{red}{-14}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-20}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+13}& = & 15 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13+2x } & = & 15 \color{red}{ -2x }\color{blue}{-13+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &17x & = &2\\\Leftrightarrow & \color{red}{17}x & = &2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12-x } & = & 12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &-15x & = &24\\\Leftrightarrow & \color{red}{-15}x & = &24\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{24}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+7}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-7x } & = & -14 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &-16x & = &-21\\\Leftrightarrow & \color{red}{-16}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-21}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{21}{16} } & & \\ & V = \left\{ \frac{21}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+7}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7-7x } & = & 1 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-15}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15-x } & = & 4 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 4 \color{blue}{+15} \\\Leftrightarrow &-4x & = &19\\\Leftrightarrow & \color{red}{-4}x & = &19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{4} } & & \\ & V = \left\{ \frac{-19}{4} \right\} & \\\end{align}\)