Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-x } & = & 11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-13}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-x } & = & -10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -10 \color{blue}{+13} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+10}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10-x } & = & 9 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & 9 \color{blue}{-10} \\\Leftrightarrow &2x & = &-1\\\Leftrightarrow & \color{red}{2}x & = &-1\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-1}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+7}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7-11x } & = & -12 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &-6x & = &-19\\\Leftrightarrow & \color{red}{-6}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{19}{6} } & & \\ & V = \left\{ \frac{19}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+6}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6+5x } & = & 2 \color{red}{ -5x }\color{blue}{-6+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &8x & = &-4\\\Leftrightarrow & \color{red}{8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-12}& = & 7 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12+10x } & = & 7 \color{red}{ -10x }\color{blue}{+12+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & 7 \color{blue}{+12} \\\Leftrightarrow &9x & = &19\\\Leftrightarrow & \color{red}{9}x & = &19\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{19}{9} \\\Leftrightarrow & \color{green}{ x = \frac{19}{9} } & & \\ & V = \left\{ \frac{19}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+15}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15-x } & = & -9 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &-3x & = &-24\\\Leftrightarrow & \color{red}{-3}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-24}{-3} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+8}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-7x } & = & -8 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &-20x & = &-16\\\Leftrightarrow & \color{red}{-20}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-16}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-2}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2+13x } & = & -11 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -11 \color{blue}{+2} \\\Leftrightarrow &23x & = &-9\\\Leftrightarrow & \color{red}{23}x & = &-9\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-9}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{23} } & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-11}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-x } & = & 14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 14 \color{blue}{+11} \\\Leftrightarrow &-11x & = &25\\\Leftrightarrow & \color{red}{-11}x & = &25\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{25}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{11} } & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-11}& = & 7 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11+4x } & = & 7 \color{red}{ -4x }\color{blue}{+11+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &13x & = &18\\\Leftrightarrow & \color{red}{13}x & = &18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+9}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9-13x } & = & -15 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &-3x & = &-24\\\Leftrightarrow & \color{red}{-3}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-24}{-3} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)