Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+11}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11-5x } & = & -1 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & 7x \color{blue}{-5x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &2x & = &-12\\\Leftrightarrow & \color{red}{2}x & = &-12\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-12}{2} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+2}& = & 8 \color{red}{ +14x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2-14x } & = & 8 \color{red}{ +14x }\color{blue}{-2-14x } \\\Leftrightarrow & 5x \color{blue}{-14x } & = & 8 \color{blue}{-2} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+3}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3+11x } & = & -3 \color{red}{ -11x }\color{blue}{-3+11x } \\\Leftrightarrow & -12x \color{blue}{+11x } & = & -3 \color{blue}{-3} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-4}& = & -5 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4-12x } & = & -5 \color{red}{ +12x }\color{blue}{+4-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+7}& = & 5 \color{red}{ -5x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7+5x } & = & 5 \color{red}{ -5x }\color{blue}{-7+5x } \\\Leftrightarrow & -8x \color{blue}{+5x } & = & 5 \color{blue}{-7} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-7}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-7}\color{blue}{+7-5x } & = & 3 \color{red}{ +5x }\color{blue}{+7-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 3 \color{blue}{+7} \\\Leftrightarrow &-19x & = &10\\\Leftrightarrow & \color{red}{-19}x & = &10\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{10}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+9}& = & -5 \color{red}{ +14x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-14x } & = & -5 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & -15x \color{blue}{-14x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &-29x & = &-14\\\Leftrightarrow & \color{red}{-29}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-29}x}{ \color{blue}{ -29}} & = & \frac{-14}{-29} \\\Leftrightarrow & \color{green}{ x = \frac{14}{29} } & & \\ & V = \left\{ \frac{14}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-14}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14-9x } & = & -14 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -14 \color{blue}{+14} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-9}& = & -6 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-9}\color{blue}{+9+8x } & = & -6 \color{red}{ -8x }\color{blue}{+9+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &11x & = &3\\\Leftrightarrow & \color{red}{11}x & = &3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+2}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2-13x } & = & 9 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & 9 \color{blue}{-2} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+8}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-11x } & = & 14 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & -6x \color{blue}{-11x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-17x & = &6\\\Leftrightarrow & \color{red}{-17}x & = &6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-8}& = & 5 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-8}\color{blue}{+8-5x } & = & 5 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 5 \color{blue}{+8} \\\Leftrightarrow &-17x & = &13\\\Leftrightarrow & \color{red}{-17}x & = &13\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{13}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{17} } & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)