Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-4}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4-x } & = & 8 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &-6x & = &12\\\Leftrightarrow & \color{red}{-6}x & = &12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{12}{-6} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+8}& = & 15 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8-4x } & = & 15 \color{red}{ +4x }\color{blue}{-8-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & 15 \color{blue}{-8} \\\Leftrightarrow &5x & = &7\\\Leftrightarrow & \color{red}{5}x & = &7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+5}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & -12 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &-15x & = &-17\\\Leftrightarrow & \color{red}{-15}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{17}{15} } & & \\ & V = \left\{ \frac{17}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+4}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-x } & = & 2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-12}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-x } & = & -1 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -1 \color{blue}{+12} \\\Leftrightarrow &-6x & = &11\\\Leftrightarrow & \color{red}{-6}x & = &11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-8}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-x } & = & 11 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 11 \color{blue}{+8} \\\Leftrightarrow &-10x & = &19\\\Leftrightarrow & \color{red}{-10}x & = &19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{10} } & & \\ & V = \left\{ \frac{-19}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+10}& = & -9 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10+8x } & = & -9 \color{red}{ -8x }\color{blue}{-10+8x } \\\Leftrightarrow & x \color{blue}{+8x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &9x & = &-19\\\Leftrightarrow & \color{red}{9}x & = &-19\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-19}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-14}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14-13x } & = & 12 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & 12 \color{blue}{+14} \\\Leftrightarrow &2x & = &26\\\Leftrightarrow & \color{red}{2}x & = &26\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{26}{2} \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4-x } & = & 5 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+12}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12-x } & = & -1 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -1 \color{blue}{-12} \\\Leftrightarrow &-7x & = &-13\\\Leftrightarrow & \color{red}{-7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-9}& = & -9 \color{red}{ -5x } \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9+5x } & = & -9 \color{red}{ -5x }\color{blue}{+9+5x } \\\Leftrightarrow & 13x \color{blue}{+5x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &18x & = &0\\\Leftrightarrow & \color{red}{18}x & = &0\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{0}{18} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+3}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-x } & = & 12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)