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

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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. \(\begin{align} & 2x \color{red}{+15}& = & -12 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-3x } & = & -12 \color{red}{ +3x }\color{blue}{-15-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &-x & = &-27\\\Leftrightarrow & \color{red}{-}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-27}{-1} \\\Leftrightarrow & \color{green}{ x = 27 } & & \\ & V = \left\{ 27 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+1}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x } & = & 1 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 1 \color{blue}{-1} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+8}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8-x } & = & -5 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -5 \color{blue}{-8} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-13}& = & -7 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13+3x } & = & -7 \color{red}{ -3x }\color{blue}{+13+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -7 \color{blue}{+13} \\\Leftrightarrow &7x & = &6\\\Leftrightarrow & \color{red}{7}x & = &6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2-x } & = & -11 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -11 \color{blue}{-2} \\\Leftrightarrow &9x & = &-13\\\Leftrightarrow & \color{red}{9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-13}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-8}& = & 15 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-8x } & = & 15 \color{red}{ +8x }\color{blue}{+8-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &-21x & = &23\\\Leftrightarrow & \color{red}{-21}x & = &23\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{23}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{21} } & & \\ & V = \left\{ \frac{-23}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+14}& = & -14 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14-2x } & = & -14 \color{red}{ +2x }\color{blue}{-14-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & -14 \color{blue}{-14} \\\Leftrightarrow &13x & = &-28\\\Leftrightarrow & \color{red}{13}x & = &-28\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-28}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{13} } & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-15}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15+2x } & = & -2 \color{red}{ -2x }\color{blue}{+15+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3-x } & = & -10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -10 \color{blue}{-3} \\\Leftrightarrow &-9x & = &-13\\\Leftrightarrow & \color{red}{-9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+1}& = & 2 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1+9x } & = & 2 \color{red}{ -9x }\color{blue}{-1+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 2 \color{blue}{-1} \\\Leftrightarrow &14x & = &1\\\Leftrightarrow & \color{red}{14}x & = &1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-3}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-x } & = & 14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &-12x & = &17\\\Leftrightarrow & \color{red}{-12}x & = &17\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{17}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{12} } & & \\ & V = \left\{ \frac{-17}{12} \right\} & \\\end{align}\)