Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-6}& = & -14 \color{red}{ +14x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-14x } & = & -14 \color{red}{ +14x }\color{blue}{+6-14x } \\\Leftrightarrow & -15x \color{blue}{-14x } & = & -14 \color{blue}{+6} \\\Leftrightarrow &-29x & = &-8\\\Leftrightarrow & \color{red}{-29}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-29}x}{ \color{blue}{ -29}} & = & \frac{-8}{-29} \\\Leftrightarrow & \color{green}{ x = \frac{8}{29} } & & \\ & V = \left\{ \frac{8}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-1}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1-13x } & = & 3 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &-x & = &4\\\Leftrightarrow & \color{red}{-}x & = &4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{4}{-1} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+12}& = & 3 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12+15x } & = & 3 \color{red}{ -15x }\color{blue}{-12+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & 3 \color{blue}{-12} \\\Leftrightarrow &14x & = &-9\\\Leftrightarrow & \color{red}{14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-9}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-12}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-5x } & = & 10 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & 7x \color{blue}{-5x } & = & 10 \color{blue}{+12} \\\Leftrightarrow &2x & = &22\\\Leftrightarrow & \color{red}{2}x & = &22\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{22}{2} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-3}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-13x } & = & 11 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & 11 \color{blue}{+3} \\\Leftrightarrow &-x & = &14\\\Leftrightarrow & \color{red}{-}x & = &14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{14}{-1} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+11}& = & 7 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11-3x } & = & 7 \color{red}{ +3x }\color{blue}{-11-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &-x & = &-4\\\Leftrightarrow & \color{red}{-}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-4}{-1} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+6}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6+11x } & = & 3 \color{red}{ -11x }\color{blue}{-6+11x } \\\Leftrightarrow & -6x \color{blue}{+11x } & = & 3 \color{blue}{-6} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-5}& = & 5 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5-12x } & = & 5 \color{red}{ +12x }\color{blue}{+5-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & 5 \color{blue}{+5} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+10}& = & 15 \color{red}{ +15x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-15x } & = & 15 \color{red}{ +15x }\color{blue}{-10-15x } \\\Leftrightarrow & 2x \color{blue}{-15x } & = & 15 \color{blue}{-10} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-11}& = & 6 \color{red}{ -6x } \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11+6x } & = & 6 \color{red}{ -6x }\color{blue}{+11+6x } \\\Leftrightarrow & -7x \color{blue}{+6x } & = & 6 \color{blue}{+11} \\\Leftrightarrow &-x & = &17\\\Leftrightarrow & \color{red}{-}x & = &17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{17}{-1} \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{-12}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12-x } & = & -6 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -6 \color{blue}{+12} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+1}& = & -14 \color{red}{ +15x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-15x } & = & -14 \color{red}{ +15x }\color{blue}{-1-15x } \\\Leftrightarrow & -7x \color{blue}{-15x } & = & -14 \color{blue}{-1} \\\Leftrightarrow &-22x & = &-15\\\Leftrightarrow & \color{red}{-22}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}} & = & \frac{-15}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{15}{22} } & & \\ & V = \left\{ \frac{15}{22} \right\} & \\\end{align}\)