Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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