Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+12}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12+13x } & = & -10 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &20x & = &-22\\\Leftrightarrow & \color{red}{20}x & = &-22\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-22}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-6}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{-6}\color{blue}{+6-11x } & = & 15 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &-13x & = &21\\\Leftrightarrow & \color{red}{-13}x & = &21\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{21}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{13} } & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-x } & = & -10 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &-7x & = &-12\\\Leftrightarrow & \color{red}{-7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-x } & = & -15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -15 \color{blue}{+1} \\\Leftrightarrow &-16x & = &-14\\\Leftrightarrow & \color{red}{-16}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-10}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-11x } & = & 2 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &-16x & = &12\\\Leftrightarrow & \color{red}{-16}x & = &12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-4}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-x } & = & 15 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 15 \color{blue}{+4} \\\Leftrightarrow &-13x & = &19\\\Leftrightarrow & \color{red}{-13}x & = &19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+4}& = & -15 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+4}\color{blue}{-4+13x } & = & -15 \color{red}{ -13x }\color{blue}{-4+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &23x & = &-19\\\Leftrightarrow & \color{red}{23}x & = &-19\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-19}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{23} } & & \\ & V = \left\{ \frac{-19}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-8}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-x } & = & 12 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &-5x & = &20\\\Leftrightarrow & \color{red}{-5}x & = &20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{20}{-5} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-x } & = & -1 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -1 \color{blue}{+13} \\\Leftrightarrow &-9x & = &12\\\Leftrightarrow & \color{red}{-9}x & = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-14}& = & -15 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14+2x } & = & -15 \color{red}{ -2x }\color{blue}{+14+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & -15 \color{blue}{+14} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+10}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10-13x } & = & -8 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -8 \color{blue}{-10} \\\Leftrightarrow &-7x & = &-18\\\Leftrightarrow & \color{red}{-7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{-13}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13-x } & = & 2 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 2 \color{blue}{+13} \\\Leftrightarrow &13x & = &15\\\Leftrightarrow & \color{red}{13}x & = &15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)