Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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