Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-4}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-x } & = & -1 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -1 \color{blue}{+4} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-8}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-x } & = & 13 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{+8} \\\Leftrightarrow &-9x & = &21\\\Leftrightarrow & \color{red}{-9}x & = &21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-12}& = & 12 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12+5x } & = & 12 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &6x & = &24\\\Leftrightarrow & \color{red}{6}x & = &24\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{24}{6} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+2}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & -12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -12 \color{blue}{-2} \\\Leftrightarrow &-4x & = &-14\\\Leftrightarrow & \color{red}{-4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-14}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-15}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+13x } & = & -14 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &20x & = &1\\\Leftrightarrow & \color{red}{20}x & = &1\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{1}{20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{20} } & & \\ & V = \left\{ \frac{1}{20} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-11}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-13x } & = & -5 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -5 \color{blue}{+11} \\\Leftrightarrow &-19x & = &6\\\Leftrightarrow & \color{red}{-19}x & = &6\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{6}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{19} } & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-10}& = & 5 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10+9x } & = & 5 \color{red}{ -9x }\color{blue}{+10+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & 5 \color{blue}{+10} \\\Leftrightarrow &8x & = &15\\\Leftrightarrow & \color{red}{8}x & = &15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+13}& = & -6 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13+3x } & = & -6 \color{red}{ -3x }\color{blue}{-13+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -6 \color{blue}{-13} \\\Leftrightarrow &13x & = &-19\\\Leftrightarrow & \color{red}{13}x & = &-19\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-19}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+9}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-x } & = & 5 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 5 \color{blue}{-9} \\\Leftrightarrow &-14x & = &-4\\\Leftrightarrow & \color{red}{-14}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-x } & = & -2 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -2 \color{blue}{-15} \\\Leftrightarrow &-10x & = &-17\\\Leftrightarrow & \color{red}{-10}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{17}{10} } & & \\ & V = \left\{ \frac{17}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{-8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-x } & = & -14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &-9x & = &-6\\\Leftrightarrow & \color{red}{-9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-4}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4-13x } & = & 9 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 9 \color{blue}{+4} \\\Leftrightarrow &-16x & = &13\\\Leftrightarrow & \color{red}{-16}x & = &13\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{13}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{16} } & & \\ & V = \left\{ \frac{-13}{16} \right\} & \\\end{align}\)