Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+15}& = & -13 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-8x } & = & -13 \color{red}{ +8x }\color{blue}{-15-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-28\\\Leftrightarrow & \color{red}{-15}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-28}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{28}{15} } & & \\ & V = \left\{ \frac{28}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-8}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-8}\color{blue}{+8-11x } & = & 14 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 14 \color{blue}{+8} \\\Leftrightarrow &-21x & = &22\\\Leftrightarrow & \color{red}{-21}x & = &22\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{22}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{21} } & & \\ & V = \left\{ \frac{-22}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-7}& = & 14 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7-8x } & = & 14 \color{red}{ +8x }\color{blue}{+7-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &-x & = &21\\\Leftrightarrow & \color{red}{-}x & = &21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{21}{-1} \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-x } & = & 9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &-16x & = &10\\\Leftrightarrow & \color{red}{-16}x & = &10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-10}& = & 14 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10-9x } & = & 14 \color{red}{ +9x }\color{blue}{+10-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 14 \color{blue}{+10} \\\Leftrightarrow &-x & = &24\\\Leftrightarrow & \color{red}{-}x & = &24\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{24}{-1} \\\Leftrightarrow & \color{green}{ x = -24 } & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-x } & = & 5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &-12x & = &9\\\Leftrightarrow & \color{red}{-12}x & = &9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+13}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-7x } & = & -1 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-14\\\Leftrightarrow & \color{red}{-13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+13}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13-x } & = & -6 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -6 \color{blue}{-13} \\\Leftrightarrow &13x & = &-19\\\Leftrightarrow & \color{red}{13}x & = &-19\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-19}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+9}& = & 14 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+9}\color{blue}{-9+4x } & = & 14 \color{red}{ -4x }\color{blue}{-9+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 14 \color{blue}{-9} \\\Leftrightarrow &9x & = &5\\\Leftrightarrow & \color{red}{9}x & = &5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+10}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10-5x } & = & -15 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & -15 \color{blue}{-10} \\\Leftrightarrow &9x & = &-25\\\Leftrightarrow & \color{red}{9}x & = &-25\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-25}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{9} } & & \\ & V = \left\{ \frac{-25}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-8}& = & -4 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-8x } & = & -4 \color{red}{ +8x }\color{blue}{+8-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &-23x & = &4\\\Leftrightarrow & \color{red}{-23}x & = &4\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{4}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{23} } & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{+13}& = & 15 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13+15x } & = & 15 \color{red}{ -15x }\color{blue}{-13+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &23x & = &2\\\Leftrightarrow & \color{red}{23}x & = &2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{2}{23} } & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)