Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+1}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-13x } & = & 6 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-25x & = &5\\\Leftrightarrow & \color{red}{-25}x & = &5\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{5}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-7}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7-13x } & = & 4 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 4 \color{blue}{+7} \\\Leftrightarrow &-5x & = &11\\\Leftrightarrow & \color{red}{-5}x & = &11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-x } & = & 12 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &-8x & = &27\\\Leftrightarrow & \color{red}{-8}x & = &27\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{27}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{8} } & & \\ & V = \left\{ \frac{-27}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-1}& = & -2 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-1}\color{blue}{+1-12x } & = & -2 \color{red}{ +12x }\color{blue}{+1-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{+8}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-11x } & = & -11 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &-21x & = &-19\\\Leftrightarrow & \color{red}{-21}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-19}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{19}{21} } & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-14}& = & 9 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14-8x } & = & 9 \color{red}{ +8x }\color{blue}{+14-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & 9 \color{blue}{+14} \\\Leftrightarrow &-13x & = &23\\\Leftrightarrow & \color{red}{-13}x & = &23\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{23}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{13} } & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+12}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12-x } & = & 13 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 13 \color{blue}{-12} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-9}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-x } & = & 6 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &-3x & = &15\\\Leftrightarrow & \color{red}{-3}x & = &15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{15}{-3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-12}& = & 5 \color{red}{ +4x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-4x } & = & 5 \color{red}{ +4x }\color{blue}{+12-4x } \\\Leftrightarrow & 7x \color{blue}{-4x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &3x & = &17\\\Leftrightarrow & \color{red}{3}x & = &17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-6}& = & 8 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6-2x } & = & 8 \color{red}{ +2x }\color{blue}{+6-2x } \\\Leftrightarrow & 13x \color{blue}{-2x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &11x & = &14\\\Leftrightarrow & \color{red}{11}x & = &14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{14}{11} } & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+15}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-13x } & = & 10 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 10 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-5\\\Leftrightarrow & \color{red}{-5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-5}{-5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-3}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-x } & = & -8 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)