Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(3x+9=9+7x\)
- \(-3x-14=7+x\)
- \(-5x-5=-12+x\)
- \(-5x+3=15+x\)
- \(9x-14=-7+10x\)
- \(5x-5=8+x\)
- \(-11x-15=1+x\)
- \(3x+10=-3-5x\)
- \(14x+3=-7+x\)
- \(-14x+1=9+3x\)
- \(-8x+5=-6+x\)
- \(3x+8=-8-8x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 3x \color{red}{+9}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9-7x }
& = & 9 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 3x \color{blue}{-7x }
& = & 9 \color{blue}{-9} \\\Leftrightarrow &-4x
& = &0\\\Leftrightarrow & \color{red}{-4}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-x }
& = & 7 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 7 \color{blue}{+14} \\\Leftrightarrow &-4x
& = &21\\\Leftrightarrow & \color{red}{-4}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{21}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{4} } & & \\ & V = \left\{ \frac{-21}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-5}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x }
& = & -12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & -12 \color{blue}{+5} \\\Leftrightarrow &-6x
& = &-7\\\Leftrightarrow & \color{red}{-6}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+3}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-x }
& = & 15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 15 \color{blue}{-3} \\\Leftrightarrow &-6x
& = &12\\\Leftrightarrow & \color{red}{-6}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{12}{-6} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-14}& = & -7 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14-10x }
& = & -7 \color{red}{ +10x }\color{blue}{+14-10x } \\\Leftrightarrow & 9x \color{blue}{-10x }
& = & -7 \color{blue}{+14} \\\Leftrightarrow &-x
& = &7\\\Leftrightarrow & \color{red}{-}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-5}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5-x }
& = & 8 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 5x \color{blue}{-x }
& = & 8 \color{blue}{+5} \\\Leftrightarrow &4x
& = &13\\\Leftrightarrow & \color{red}{4}x
& = &13\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{13}{4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-15}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x }
& = & 1 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 1 \color{blue}{+15} \\\Leftrightarrow &-12x
& = &16\\\Leftrightarrow & \color{red}{-12}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+10}& = & -3 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10+5x }
& = & -3 \color{red}{ -5x }\color{blue}{-10+5x } \\\Leftrightarrow & 3x \color{blue}{+5x }
& = & -3 \color{blue}{-10} \\\Leftrightarrow &8x
& = &-13\\\Leftrightarrow & \color{red}{8}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{-13}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+3}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3-x }
& = & -7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & -7 \color{blue}{-3} \\\Leftrightarrow &13x
& = &-10\\\Leftrightarrow & \color{red}{13}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+1}& = & 9 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-3x }
& = & 9 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & -14x \color{blue}{-3x }
& = & 9 \color{blue}{-1} \\\Leftrightarrow &-17x
& = &8\\\Leftrightarrow & \color{red}{-17}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{17} } & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+5}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5-x }
& = & -6 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & -6 \color{blue}{-5} \\\Leftrightarrow &-9x
& = &-11\\\Leftrightarrow & \color{red}{-9}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+8}& = & -8 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8+8x }
& = & -8 \color{red}{ -8x }\color{blue}{-8+8x } \\\Leftrightarrow & 3x \color{blue}{+8x }
& = & -8 \color{blue}{-8} \\\Leftrightarrow &11x
& = &-16\\\Leftrightarrow & \color{red}{11}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)