Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-12}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12-11x } & = & 3 \color{red}{ +11x }\color{blue}{+12-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &-6x & = &15\\\Leftrightarrow & \color{red}{-6}x & = &15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-15}& = & 13 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15+5x } & = & 13 \color{red}{ -5x }\color{blue}{+15+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 13 \color{blue}{+15} \\\Leftrightarrow &8x & = &28\\\Leftrightarrow & \color{red}{8}x & = &28\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{28}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+15}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15-7x } & = & -4 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -4 \color{blue}{-15} \\\Leftrightarrow &-17x & = &-19\\\Leftrightarrow & \color{red}{-17}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-19}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{19}{17} } & & \\ & V = \left\{ \frac{19}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+5}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5-x } & = & -12 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &-9x & = &-17\\\Leftrightarrow & \color{red}{-9}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-17}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-9}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9-x } & = & -15 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -15 \color{blue}{+9} \\\Leftrightarrow &-9x & = &-6\\\Leftrightarrow & \color{red}{-9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-x } & = & -8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &-6x & = &-20\\\Leftrightarrow & \color{red}{-6}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-20}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-x } & = & -9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-6x & = &-14\\\Leftrightarrow & \color{red}{-6}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1-x } & = & 6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &12x & = &5\\\Leftrightarrow & \color{red}{12}x & = &5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+15}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-x } & = & -3 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -3 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-18\\\Leftrightarrow & \color{red}{-5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+13}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13+11x } & = & -14 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -14 \color{blue}{-13} \\\Leftrightarrow &23x & = &-27\\\Leftrightarrow & \color{red}{23}x & = &-27\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-27}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{23} } & & \\ & V = \left\{ \frac{-27}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+12}& = & -10 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12+4x } & = & -10 \color{red}{ -4x }\color{blue}{-12+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &9x & = &-22\\\Leftrightarrow & \color{red}{9}x & = &-22\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-22}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{9} } & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{+5}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-x } & = & -11 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &-11x & = &-16\\\Leftrightarrow & \color{red}{-11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)