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