Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(13x+5=9+6x\)
- \(4x+3=1+5x\)
- \(5x-3=14+13x\)
- \(-13x+14=-1+7x\)
- \(10x-9=13+x\)
- \(6x-9=-12+13x\)
- \(-9x-14=-11+x\)
- \(-6x+4=-14+7x\)
- \(9x+12=-15-8x\)
- \(3x-12=-8+x\)
- \(-11x-2=-5+x\)
- \(-12x-8=-8+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 13x \color{red}{+5}& = & 9 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5-6x }
& = & 9 \color{red}{ +6x }\color{blue}{-5-6x } \\\Leftrightarrow & 13x \color{blue}{-6x }
& = & 9 \color{blue}{-5} \\\Leftrightarrow &7x
& = &4\\\Leftrightarrow & \color{red}{7}x
& = &4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+3}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3-5x }
& = & 1 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 4x \color{blue}{-5x }
& = & 1 \color{blue}{-3} \\\Leftrightarrow &-x
& = &-2\\\Leftrightarrow & \color{red}{-}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-2}{-1} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-3}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3-13x }
& = & 14 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & 5x \color{blue}{-13x }
& = & 14 \color{blue}{+3} \\\Leftrightarrow &-8x
& = &17\\\Leftrightarrow & \color{red}{-8}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{8} } & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+14}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-7x }
& = & -1 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & -13x \color{blue}{-7x }
& = & -1 \color{blue}{-14} \\\Leftrightarrow &-20x
& = &-15\\\Leftrightarrow & \color{red}{-20}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{-15}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9-x }
& = & 13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 10x \color{blue}{-x }
& = & 13 \color{blue}{+9} \\\Leftrightarrow &9x
& = &22\\\Leftrightarrow & \color{red}{9}x
& = &22\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{22}{9} \\\Leftrightarrow & \color{green}{ x = \frac{22}{9} } & & \\ & V = \left\{ \frac{22}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-9}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{-9}\color{blue}{+9-13x }
& = & -12 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 6x \color{blue}{-13x }
& = & -12 \color{blue}{+9} \\\Leftrightarrow &-7x
& = &-3\\\Leftrightarrow & \color{red}{-7}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-14}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-x }
& = & -11 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -11 \color{blue}{+14} \\\Leftrightarrow &-10x
& = &3\\\Leftrightarrow & \color{red}{-10}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+4}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-7x }
& = & -14 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & -14 \color{blue}{-4} \\\Leftrightarrow &-13x
& = &-18\\\Leftrightarrow & \color{red}{-13}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+12}& = & -15 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12+8x }
& = & -15 \color{red}{ -8x }\color{blue}{-12+8x } \\\Leftrightarrow & 9x \color{blue}{+8x }
& = & -15 \color{blue}{-12} \\\Leftrightarrow &17x
& = &-27\\\Leftrightarrow & \color{red}{17}x
& = &-27\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-27}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{17} } & & \\ & V = \left\{ \frac{-27}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12-x }
& = & -8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 3x \color{blue}{-x }
& = & -8 \color{blue}{+12} \\\Leftrightarrow &2x
& = &4\\\Leftrightarrow & \color{red}{2}x
& = &4\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{4}{2} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-2}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-x }
& = & -5 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -5 \color{blue}{+2} \\\Leftrightarrow &-12x
& = &-3\\\Leftrightarrow & \color{red}{-12}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-8}\color{blue}{+8-x }
& = & -8 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -8 \color{blue}{+8} \\\Leftrightarrow &-13x
& = &0\\\Leftrightarrow & \color{red}{-13}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)