Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-8}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-x } & = & 8 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &-10x & = &16\\\Leftrightarrow & \color{red}{-10}x & = &16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+2}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2-x } & = & 1 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 1 \color{blue}{-2} \\\Leftrightarrow &9x & = &-1\\\Leftrightarrow & \color{red}{9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-8}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-8}\color{blue}{+8-x } & = & 11 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 11 \color{blue}{+8} \\\Leftrightarrow &-13x & = &19\\\Leftrightarrow & \color{red}{-13}x & = &19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+6}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6-11x } & = & 3 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 13x \color{blue}{-11x } & = & 3 \color{blue}{-6} \\\Leftrightarrow &2x & = &-3\\\Leftrightarrow & \color{red}{2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-8}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-x } & = & -9 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -9 \color{blue}{+8} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+14}& = & -8 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-14x } & = & -8 \color{red}{ +14x }\color{blue}{-14-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -8 \color{blue}{-14} \\\Leftrightarrow &-23x & = &-22\\\Leftrightarrow & \color{red}{-23}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-22}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{22}{23} } & & \\ & V = \left\{ \frac{22}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-5}& = & 14 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-5}\color{blue}{+5-10x } & = & 14 \color{red}{ +10x }\color{blue}{+5-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &-13x & = &19\\\Leftrightarrow & \color{red}{-13}x & = &19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+13}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & -5 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-18\\\Leftrightarrow & \color{red}{-11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+12}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-x } & = & 14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+10}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-x } & = & -5 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &-10x & = &-15\\\Leftrightarrow & \color{red}{-10}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-15}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-x } & = & 7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-11}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-11}\color{blue}{+11-x } & = & -6 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -6 \color{blue}{+11} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)