Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+13}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13-7x } & = & -14 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & 11x \color{blue}{-7x } & = & -14 \color{blue}{-13} \\\Leftrightarrow &4x & = &-27\\\Leftrightarrow & \color{red}{4}x & = &-27\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-27}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{4} } & & \\ & V = \left\{ \frac{-27}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-7}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-x } & = & 9 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 9 \color{blue}{+7} \\\Leftrightarrow &-5x & = &16\\\Leftrightarrow & \color{red}{-5}x & = &16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4-x } & = & 5 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &-6x & = &1\\\Leftrightarrow & \color{red}{-6}x & = &1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+8}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8-3x } & = & 14 \color{red}{ +3x }\color{blue}{-8-3x } \\\Leftrightarrow & -x \color{blue}{-3x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-4x & = &6\\\Leftrightarrow & \color{red}{-4}x & = &6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4-x } & = & -8 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &13x & = &-4\\\Leftrightarrow & \color{red}{13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+8}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-13x } & = & 14 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+8}& = & -6 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8-12x } & = & -6 \color{red}{ +12x }\color{blue}{-8-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & -6 \color{blue}{-8} \\\Leftrightarrow &-13x & = &-14\\\Leftrightarrow & \color{red}{-13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-8}& = & -10 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-8x } & = & -10 \color{red}{ +8x }\color{blue}{+8-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & -10 \color{blue}{+8} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+10}& = & 8 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-14x } & = & 8 \color{red}{ +14x }\color{blue}{-10-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 8 \color{blue}{-10} \\\Leftrightarrow &-25x & = &-2\\\Leftrightarrow & \color{red}{-25}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-2}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{2}{25} } & & \\ & V = \left\{ \frac{2}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+7}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-x } & = & 1 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &-9x & = &-6\\\Leftrightarrow & \color{red}{-9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+2}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2-11x } & = & 13 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &-2x & = &11\\\Leftrightarrow & \color{red}{-2}x & = &11\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{11}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+12}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12-x } & = & -2 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -2 \color{blue}{-12} \\\Leftrightarrow &-14x & = &-14\\\Leftrightarrow & \color{red}{-14}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-14}{-14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)