Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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