Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-7}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-7}\color{blue}{+7-x } & = & 2 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 2 \color{blue}{+7} \\\Leftrightarrow &-9x & = &9\\\Leftrightarrow & \color{red}{-9}x & = &9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{9}{-9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-8}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8+13x } & = & 8 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &27x & = &16\\\Leftrightarrow & \color{red}{27}x & = &16\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{16}{27} \\\Leftrightarrow & \color{green}{ x = \frac{16}{27} } & & \\ & V = \left\{ \frac{16}{27} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-10}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10-x } & = & -7 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-6}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6+13x } & = & -14 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -14 \color{blue}{+6} \\\Leftrightarrow &20x & = &-8\\\Leftrightarrow & \color{red}{20}x & = &-8\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-8}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+10}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-x } & = & -3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &-6x & = &-13\\\Leftrightarrow & \color{red}{-6}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+6}& = & -2 \color{red}{ -5x } \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6+5x } & = & -2 \color{red}{ -5x }\color{blue}{-6+5x } \\\Leftrightarrow & 13x \color{blue}{+5x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &18x & = &-8\\\Leftrightarrow & \color{red}{18}x & = &-8\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{-8}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-5}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x } & = & -2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -2 \color{blue}{+5} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+8}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8-5x } & = & 2 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &6x & = &-6\\\Leftrightarrow & \color{red}{6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-6}{6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-15}& = & 4 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-6x } & = & 4 \color{red}{ +6x }\color{blue}{+15-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 4 \color{blue}{+15} \\\Leftrightarrow &-11x & = &19\\\Leftrightarrow & \color{red}{-11}x & = &19\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{19}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{11} } & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-7}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7+7x } & = & -3 \color{red}{ -7x }\color{blue}{+7+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &15x & = &4\\\Leftrightarrow & \color{red}{15}x & = &4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-7}& = & -8 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{-7}\color{blue}{+7-3x } & = & -8 \color{red}{ +3x }\color{blue}{+7-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &-17x & = &-1\\\Leftrightarrow & \color{red}{-17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-6}& = & 15 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-6}\color{blue}{+6+5x } & = & 15 \color{red}{ -5x }\color{blue}{+6+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &11x & = &21\\\Leftrightarrow & \color{red}{11}x & = &21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)