Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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