Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+9}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9+11x } & = & 6 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 6 \color{blue}{-9} \\\Leftrightarrow &23x & = &-3\\\Leftrightarrow & \color{red}{23}x & = &-3\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-3}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{23} } & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-5}& = & 13 \color{red}{ +3x } \\\Leftrightarrow & x \color{red}{-5}\color{blue}{+5-3x } & = & 13 \color{red}{ +3x }\color{blue}{+5-3x } \\\Leftrightarrow & x \color{blue}{-3x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-2x & = &18\\\Leftrightarrow & \color{red}{-2}x & = &18\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{18}{-2} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1-x } & = & -12 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -12 \color{blue}{+1} \\\Leftrightarrow &-7x & = &-11\\\Leftrightarrow & \color{red}{-7}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+2}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2-11x } & = & -15 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -15 \color{blue}{-2} \\\Leftrightarrow &-6x & = &-17\\\Leftrightarrow & \color{red}{-6}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+1}& = & 5 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1+11x } & = & 5 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &26x & = &4\\\Leftrightarrow & \color{red}{26}x & = &4\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{4}{26} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+9}& = & 2 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9+10x } & = & 2 \color{red}{ -10x }\color{blue}{-9+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &21x & = &-7\\\Leftrightarrow & \color{red}{21}x & = &-7\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-7}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-14}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-x } & = & 2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &-10x & = &16\\\Leftrightarrow & \color{red}{-10}x & = &16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+3}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3-13x } & = & 2 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &-10x & = &-1\\\Leftrightarrow & \color{red}{-10}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+6}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6-9x } & = & 13 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & -x \color{blue}{-9x } & = & 13 \color{blue}{-6} \\\Leftrightarrow &-10x & = &7\\\Leftrightarrow & \color{red}{-10}x & = &7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6-x } & = & 9 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 9 \color{blue}{+6} \\\Leftrightarrow &-11x & = &15\\\Leftrightarrow & \color{red}{-11}x & = &15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-12}& = & -10 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12-5x } & = & -10 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &-x & = &2\\\Leftrightarrow & \color{red}{-}x & = &2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{2}{-1} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-14}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14+11x } & = & -3 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & -x \color{blue}{+11x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &10x & = &11\\\Leftrightarrow & \color{red}{10}x & = &11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)