Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+11}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11-5x } & = & -11 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & 7x \color{blue}{-5x } & = & -11 \color{blue}{-11} \\\Leftrightarrow &2x & = &-22\\\Leftrightarrow & \color{red}{2}x & = &-22\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-22}{2} \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+5}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+5}\color{blue}{-5-3x } & = & 3 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &-x & = &-2\\\Leftrightarrow & \color{red}{-}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-2}{-1} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-8}& = & -8 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8-10x } & = & -8 \color{red}{ +10x }\color{blue}{+8-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -8 \color{blue}{+8} \\\Leftrightarrow &-x & = &0\\\Leftrightarrow & \color{red}{-}x & = &0\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{0}{-1} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+14}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-x } & = & -1 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-6x & = &-15\\\Leftrightarrow & \color{red}{-6}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-12}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-x } & = & -14 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-6}& = & -5 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6+15x } & = & -5 \color{red}{ -15x }\color{blue}{+6+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &19x & = &1\\\Leftrightarrow & \color{red}{19}x & = &1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+14}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-7x } & = & 15 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 15 \color{blue}{-14} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-15}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-15}\color{blue}{+15-x } & = & -3 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -3 \color{blue}{+15} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+1}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1-11x } & = & -1 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -1 \color{blue}{-1} \\\Leftrightarrow &-5x & = &-2\\\Leftrightarrow & \color{red}{-5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-9}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-13x } & = & 2 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 2 \color{blue}{+9} \\\Leftrightarrow &-17x & = &11\\\Leftrightarrow & \color{red}{-17}x & = &11\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{11}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{17} } & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+13}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13-7x } & = & -12 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -12 \color{blue}{-13} \\\Leftrightarrow &3x & = &-25\\\Leftrightarrow & \color{red}{3}x & = &-25\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-25}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{3} } & & \\ & V = \left\{ \frac{-25}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-1}& = & -2 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1+13x } & = & -2 \color{red}{ -13x }\color{blue}{+1+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &22x & = &-1\\\Leftrightarrow & \color{red}{22}x & = &-1\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-1}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{22} } & & \\ & V = \left\{ \frac{-1}{22} \right\} & \\\end{align}\)