Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-13}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13-3x } & = & 3 \color{red}{ +3x }\color{blue}{+13-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 3 \color{blue}{+13} \\\Leftrightarrow &5x & = &16\\\Leftrightarrow & \color{red}{5}x & = &16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-14}& = & 8 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14+9x } & = & 8 \color{red}{ -9x }\color{blue}{+14+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & 8 \color{blue}{+14} \\\Leftrightarrow &8x & = &22\\\Leftrightarrow & \color{red}{8}x & = &22\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{22}{8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-8}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8-7x } & = & -7 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -7 \color{blue}{+8} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-9}& = & -4 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9-12x } & = & -4 \color{red}{ +12x }\color{blue}{+9-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & -4 \color{blue}{+9} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12-x } & = & 7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 7 \color{blue}{+12} \\\Leftrightarrow &-15x & = &19\\\Leftrightarrow & \color{red}{-15}x & = &19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{15} } & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+6}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6-9x } & = & 4 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 4 \color{blue}{-6} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-15}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-x } & = & 10 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &-16x & = &25\\\Leftrightarrow & \color{red}{-16}x & = &25\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{25}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{16} } & & \\ & V = \left\{ \frac{-25}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-12}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-7x } & = & -14 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+4}& = & -8 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4+8x } & = & -8 \color{red}{ -8x }\color{blue}{-4+8x } \\\Leftrightarrow & -x \color{blue}{+8x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &7x & = &-12\\\Leftrightarrow & \color{red}{7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-4}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-4}\color{blue}{+4-x } & = & 12 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &-14x & = &16\\\Leftrightarrow & \color{red}{-14}x & = &16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-10}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10+13x } & = & -3 \color{red}{ -13x }\color{blue}{+10+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -3 \color{blue}{+10} \\\Leftrightarrow &27x & = &7\\\Leftrightarrow & \color{red}{27}x & = &7\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{7}{27} \\\Leftrightarrow & \color{green}{ x = \frac{7}{27} } & & \\ & V = \left\{ \frac{7}{27} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-5}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5-x } & = & 9 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 9 \color{blue}{+5} \\\Leftrightarrow &-12x & = &14\\\Leftrightarrow & \color{red}{-12}x & = &14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)