Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+9}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-x } & = & -12 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{-9} \\\Leftrightarrow &-11x & = &-21\\\Leftrightarrow & \color{red}{-11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+3}& = & -5 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3+9x } & = & -5 \color{red}{ -9x }\color{blue}{-3+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -5 \color{blue}{-3} \\\Leftrightarrow &19x & = &-8\\\Leftrightarrow & \color{red}{19}x & = &-8\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-8}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-13}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-13x } & = & 3 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 3 \color{blue}{+13} \\\Leftrightarrow &-16x & = &16\\\Leftrightarrow & \color{red}{-16}x & = &16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{16}{-16} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-4}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4+11x } & = & -14 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & x \color{blue}{+11x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &12x & = &-10\\\Leftrightarrow & \color{red}{12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-10}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-6}\color{blue}{+6-x } & = & 6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &-3x & = &12\\\Leftrightarrow & \color{red}{-3}x & = &12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{12}{-3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+3}& = & 12 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-3x } & = & 12 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &-8x & = &9\\\Leftrightarrow & \color{red}{-8}x & = &9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+10}& = & 7 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10+7x } & = & 7 \color{red}{ -7x }\color{blue}{-10+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &18x & = &-3\\\Leftrightarrow & \color{red}{18}x & = &-3\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{-3}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-6}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6-x } & = & -14 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -14 \color{blue}{+6} \\\Leftrightarrow &-10x & = &-8\\\Leftrightarrow & \color{red}{-10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6-x } & = & 3 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 3 \color{blue}{-6} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-7}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7-x } & = & -3 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{-7}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-7}\color{blue}{+7-x } & = & -3 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+5}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-x } & = & -4 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -4 \color{blue}{-5} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)