Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(x-11=9-2x\)
- \(-12x+1=-5+13x\)
- \(-12x-6=-7+13x\)
- \(8x-4=-7+7x\)
- \(10x+8=-14+11x\)
- \(-7x+9=-9+x\)
- \(x+9=5+6x\)
- \(4x+8=8+x\)
- \(-9x-8=4+x\)
- \(-11x+9=10+x\)
- \(-13x-12=-8+x\)
- \(9x+6=-7+2x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & x \color{red}{-11}& = & 9 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11+2x }
& = & 9 \color{red}{ -2x }\color{blue}{+11+2x } \\\Leftrightarrow & x \color{blue}{+2x }
& = & 9 \color{blue}{+11} \\\Leftrightarrow &3x
& = &20\\\Leftrightarrow & \color{red}{3}x
& = &20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+1}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-13x }
& = & -5 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & -5 \color{blue}{-1} \\\Leftrightarrow &-25x
& = &-6\\\Leftrightarrow & \color{red}{-25}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-6}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{6}{25} } & & \\ & V = \left\{ \frac{6}{25} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-6}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-13x }
& = & -7 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & -7 \color{blue}{+6} \\\Leftrightarrow &-25x
& = &-1\\\Leftrightarrow & \color{red}{-25}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-1}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{25} } & & \\ & V = \left\{ \frac{1}{25} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-4}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4-7x }
& = & -7 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & 8x \color{blue}{-7x }
& = & -7 \color{blue}{+4} \\\Leftrightarrow &x
& = &-3\\\Leftrightarrow & \color{red}{}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+8}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8-11x }
& = & -14 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 10x \color{blue}{-11x }
& = & -14 \color{blue}{-8} \\\Leftrightarrow &-x
& = &-22\\\Leftrightarrow & \color{red}{-}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-22}{-1} \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x }
& = & -9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -9 \color{blue}{-9} \\\Leftrightarrow &-8x
& = &-18\\\Leftrightarrow & \color{red}{-8}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-18}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+9}& = & 5 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9-6x }
& = & 5 \color{red}{ +6x }\color{blue}{-9-6x } \\\Leftrightarrow & x \color{blue}{-6x }
& = & 5 \color{blue}{-9} \\\Leftrightarrow &-5x
& = &-4\\\Leftrightarrow & \color{red}{-5}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+8}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8-x }
& = & 8 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 4x \color{blue}{-x }
& = & 8 \color{blue}{-8} \\\Leftrightarrow &3x
& = &0\\\Leftrightarrow & \color{red}{3}x
& = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-x }
& = & 4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 4 \color{blue}{+8} \\\Leftrightarrow &-10x
& = &12\\\Leftrightarrow & \color{red}{-10}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{12}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+9}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-x }
& = & 10 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 10 \color{blue}{-9} \\\Leftrightarrow &-12x
& = &1\\\Leftrightarrow & \color{red}{-12}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-x }
& = & -8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -8 \color{blue}{+12} \\\Leftrightarrow &-14x
& = &4\\\Leftrightarrow & \color{red}{-14}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+6}& = & -7 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6-2x }
& = & -7 \color{red}{ +2x }\color{blue}{-6-2x } \\\Leftrightarrow & 9x \color{blue}{-2x }
& = & -7 \color{blue}{-6} \\\Leftrightarrow &7x
& = &-13\\\Leftrightarrow & \color{red}{7}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{-13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)