Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+10}& = & -5 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10+7x } & = & -5 \color{red}{ -7x }\color{blue}{-10+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &12x & = &-15\\\Leftrightarrow & \color{red}{12}x & = &-15\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-15}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x } & = & -10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -10 \color{blue}{+2} \\\Leftrightarrow &-8x & = &-8\\\Leftrightarrow & \color{red}{-8}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-8}{-8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+5}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & -10 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -10 \color{blue}{-5} \\\Leftrightarrow &-12x & = &-15\\\Leftrightarrow & \color{red}{-12}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+6}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6+11x } & = & 9 \color{red}{ -11x }\color{blue}{-6+11x } \\\Leftrightarrow & -x \color{blue}{+11x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &10x & = &3\\\Leftrightarrow & \color{red}{10}x & = &3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-13}& = & 7 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-14x } & = & 7 \color{red}{ +14x }\color{blue}{+13-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &-25x & = &20\\\Leftrightarrow & \color{red}{-25}x & = &20\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{20}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-6}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6-x } & = & -13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -13 \color{blue}{+6} \\\Leftrightarrow &11x & = &-7\\\Leftrightarrow & \color{red}{11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+14}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-x } & = & -13 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &-14x & = &-27\\\Leftrightarrow & \color{red}{-14}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-27}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{27}{14} } & & \\ & V = \left\{ \frac{27}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+4}& = & 9 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+4}\color{blue}{-4+8x } & = & 9 \color{red}{ -8x }\color{blue}{-4+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 9 \color{blue}{-4} \\\Leftrightarrow &17x & = &5\\\Leftrightarrow & \color{red}{17}x & = &5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{5}{17} } & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-x } & = & -9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-16x & = &-14\\\Leftrightarrow & \color{red}{-16}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{-2}& = & 14 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{-2}\color{blue}{+2-6x } & = & 14 \color{red}{ +6x }\color{blue}{+2-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & 14 \color{blue}{+2} \\\Leftrightarrow &-5x & = &16\\\Leftrightarrow & \color{red}{-5}x & = &16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+13}& = & -14 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13-10x } & = & -14 \color{red}{ +10x }\color{blue}{-13-10x } \\\Leftrightarrow & x \color{blue}{-10x } & = & -14 \color{blue}{-13} \\\Leftrightarrow &-9x & = &-27\\\Leftrightarrow & \color{red}{-9}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-27}{-9} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+4}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-5x } & = & -12 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & -12 \color{blue}{-4} \\\Leftrightarrow &-19x & = &-16\\\Leftrightarrow & \color{red}{-19}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-16}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{16}{19} } & & \\ & V = \left\{ \frac{16}{19} \right\} & \\\end{align}\)