Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-13}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13-9x } & = & -4 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & -4 \color{blue}{+13} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+15}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15+11x } & = & -7 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &17x & = &-22\\\Leftrightarrow & \color{red}{17}x & = &-22\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-22}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{17} } & & \\ & V = \left\{ \frac{-22}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+1}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1-11x } & = & -5 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -5 \color{blue}{-1} \\\Leftrightarrow &-6x & = &-6\\\Leftrightarrow & \color{red}{-6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-6}{-6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-10}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10-7x } & = & -1 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &2x & = &9\\\Leftrightarrow & \color{red}{2}x & = &9\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{9}{2} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-10}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-x } & = & -5 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -5 \color{blue}{+10} \\\Leftrightarrow &-9x & = &5\\\Leftrightarrow & \color{red}{-9}x & = &5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+1}& = & -2 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1-14x } & = & -2 \color{red}{ +14x }\color{blue}{-1-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+1}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1+5x } & = & 2 \color{red}{ -5x }\color{blue}{-1+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 2 \color{blue}{-1} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+6}& = & -7 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6-6x } & = & -7 \color{red}{ +6x }\color{blue}{-6-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &x & = &-13\\\Leftrightarrow & \color{red}{}x & = &-13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -13 \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-3}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-x } & = & -13 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -13 \color{blue}{+3} \\\Leftrightarrow &-8x & = &-10\\\Leftrightarrow & \color{red}{-8}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-3}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-x } & = & 15 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 15 \color{blue}{+3} \\\Leftrightarrow &-13x & = &18\\\Leftrightarrow & \color{red}{-13}x & = &18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+13}& = & 6 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13+9x } & = & 6 \color{red}{ -9x }\color{blue}{-13+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &23x & = &-7\\\Leftrightarrow & \color{red}{23}x & = &-7\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-7}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{23} } & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+15}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15+7x } & = & -13 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &22x & = &-28\\\Leftrightarrow & \color{red}{22}x & = &-28\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-28}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)