Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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