Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-12}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12-x } & = & -2 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &-12x & = &10\\\Leftrightarrow & \color{red}{-12}x & = &10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-6}& = & 8 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6-8x } & = & 8 \color{red}{ +8x }\color{blue}{+6-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &-7x & = &14\\\Leftrightarrow & \color{red}{-7}x & = &14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{14}{-7} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-15}& = & -7 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15+13x } & = & -7 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &22x & = &8\\\Leftrightarrow & \color{red}{22}x & = &8\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{8}{22} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-12}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-3x } & = & 5 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & 7x \color{blue}{-3x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &4x & = &17\\\Leftrightarrow & \color{red}{4}x & = &17\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{17}{4} \\\Leftrightarrow & \color{green}{ x = \frac{17}{4} } & & \\ & V = \left\{ \frac{17}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+7}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7-13x } & = & 2 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 2 \color{blue}{-7} \\\Leftrightarrow &-25x & = &-5\\\Leftrightarrow & \color{red}{-25}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-5}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+2}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-13x } & = & 3 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 3 \color{blue}{-2} \\\Leftrightarrow &-19x & = &1\\\Leftrightarrow & \color{red}{-19}x & = &1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+1}& = & -5 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1-12x } & = & -5 \color{red}{ +12x }\color{blue}{-1-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & -5 \color{blue}{-1} \\\Leftrightarrow &-13x & = &-6\\\Leftrightarrow & \color{red}{-13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-4}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4-3x } & = & 15 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 15 \color{blue}{+4} \\\Leftrightarrow &5x & = &19\\\Leftrightarrow & \color{red}{5}x & = &19\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{19}{5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-8}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8-x } & = & -7 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -7 \color{blue}{+8} \\\Leftrightarrow &-3x & = &1\\\Leftrightarrow & \color{red}{-3}x & = &1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-5}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-x } & = & -7 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-x } & = & -10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -10 \color{blue}{-3} \\\Leftrightarrow &-15x & = &-13\\\Leftrightarrow & \color{red}{-15}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+13}& = & -2 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13-4x } & = & -2 \color{red}{ +4x }\color{blue}{-13-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & -2 \color{blue}{-13} \\\Leftrightarrow &9x & = &-15\\\Leftrightarrow & \color{red}{9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-15}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)