Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-3}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3-5x } & = & 11 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & 11 \color{blue}{+3} \\\Leftrightarrow &3x & = &14\\\Leftrightarrow & \color{red}{3}x & = &14\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{14}{3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-14}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & 2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &-15x & = &16\\\Leftrightarrow & \color{red}{-15}x & = &16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+10}& = & -4 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10+13x } & = & -4 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -4 \color{blue}{-10} \\\Leftrightarrow &20x & = &-14\\\Leftrightarrow & \color{red}{20}x & = &-14\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-14}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-3}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3-x } & = & -2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &12x & = &1\\\Leftrightarrow & \color{red}{12}x & = &1\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{1}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+3}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3-7x } & = & 14 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &2x & = &11\\\Leftrightarrow & \color{red}{2}x & = &11\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{11}{2} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+14}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-x } & = & 2 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &-14x & = &-12\\\Leftrightarrow & \color{red}{-14}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+1}& = & -1 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1+13x } & = & -1 \color{red}{ -13x }\color{blue}{-1+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -1 \color{blue}{-1} \\\Leftrightarrow &24x & = &-2\\\Leftrightarrow & \color{red}{24}x & = &-2\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-2}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-7}& = & -6 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7+15x } & = & -6 \color{red}{ -15x }\color{blue}{+7+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & -6 \color{blue}{+7} \\\Leftrightarrow &14x & = &1\\\Leftrightarrow & \color{red}{14}x & = &1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+10}& = & -4 \color{red}{ -6x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10+6x } & = & -4 \color{red}{ -6x }\color{blue}{-10+6x } \\\Leftrightarrow & x \color{blue}{+6x } & = & -4 \color{blue}{-10} \\\Leftrightarrow &7x & = &-14\\\Leftrightarrow & \color{red}{7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-14}{7} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14-x } & = & -6 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -6 \color{blue}{+14} \\\Leftrightarrow &-13x & = &8\\\Leftrightarrow & \color{red}{-13}x & = &8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+9}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-11x } & = & -10 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -10 \color{blue}{-9} \\\Leftrightarrow &-21x & = &-19\\\Leftrightarrow & \color{red}{-21}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-19}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{19}{21} } & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+7}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7+11x } & = & 7 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & -x \color{blue}{+11x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &10x & = &0\\\Leftrightarrow & \color{red}{10}x & = &0\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{0}{10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)