Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+11}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-9x } & = & -10 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -10 \color{blue}{-11} \\\Leftrightarrow &-17x & = &-21\\\Leftrightarrow & \color{red}{-17}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-21}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{21}{17} } & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-5}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x } & = & -11 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -11 \color{blue}{+5} \\\Leftrightarrow &-6x & = &-6\\\Leftrightarrow & \color{red}{-6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-6}{-6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-9}& = & -11 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9+14x } & = & -11 \color{red}{ -14x }\color{blue}{+9+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &19x & = &-2\\\Leftrightarrow & \color{red}{19}x & = &-2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-13}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-13}\color{blue}{+13-7x } & = & -7 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & -7 \color{blue}{+13} \\\Leftrightarrow &2x & = &6\\\Leftrightarrow & \color{red}{2}x & = &6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{6}{2} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+9}& = & -6 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9+13x } & = & -6 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & x \color{blue}{+13x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &14x & = &-15\\\Leftrightarrow & \color{red}{14}x & = &-15\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-15}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{14} } & & \\ & V = \left\{ \frac{-15}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-x } & = & 10 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 10 \color{blue}{+12} \\\Leftrightarrow &-13x & = &22\\\Leftrightarrow & \color{red}{-13}x & = &22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{13} } & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+14}& = & -12 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14-12x } & = & -12 \color{red}{ +12x }\color{blue}{-14-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-26\\\Leftrightarrow & \color{red}{-11}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-26}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{26}{11} } & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-11}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11-5x } & = & 8 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & 8 \color{blue}{+11} \\\Leftrightarrow &3x & = &19\\\Leftrightarrow & \color{red}{3}x & = &19\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{19}{3} \\\Leftrightarrow & \color{green}{ x = \frac{19}{3} } & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-4}& = & -13 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4-4x } & = & -13 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -13 \color{blue}{+4} \\\Leftrightarrow &5x & = &-9\\\Leftrightarrow & \color{red}{5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-10}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10-x } & = & 6 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 6 \color{blue}{+10} \\\Leftrightarrow &11x & = &16\\\Leftrightarrow & \color{red}{11}x & = &16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+2}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2-7x } & = & -2 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -2 \color{blue}{-2} \\\Leftrightarrow &8x & = &-4\\\Leftrightarrow & \color{red}{8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & 13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &-11x & = &23\\\Leftrightarrow & \color{red}{-11}x & = &23\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{23}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{11} } & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)