Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-7x+14=-3+4x\)
- \(6x+15=6+11x\)
- \(-8x-9=3+x\)
- \(-2x-10=9+x\)
- \(-10x-3=14+x\)
- \(9x+9=9+11x\)
- \(-4x-3=12+9x\)
- \(-14x+3=-7+x\)
- \(-12x+1=2+x\)
- \(9x-2=11-11x\)
- \(x-1=4+9x\)
- \(x-12=-10+12x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -7x \color{red}{+14}& = & -3 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-4x }
& = & -3 \color{red}{ +4x }\color{blue}{-14-4x } \\\Leftrightarrow & -7x \color{blue}{-4x }
& = & -3 \color{blue}{-14} \\\Leftrightarrow &-11x
& = &-17\\\Leftrightarrow & \color{red}{-11}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+15}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15-11x }
& = & 6 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 6x \color{blue}{-11x }
& = & 6 \color{blue}{-15} \\\Leftrightarrow &-5x
& = &-9\\\Leftrightarrow & \color{red}{-5}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-9}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9-x }
& = & 3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 3 \color{blue}{+9} \\\Leftrightarrow &-9x
& = &12\\\Leftrightarrow & \color{red}{-9}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-10}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-x }
& = & 9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & 9 \color{blue}{+10} \\\Leftrightarrow &-3x
& = &19\\\Leftrightarrow & \color{red}{-3}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{19}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{3} } & & \\ & V = \left\{ \frac{-19}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-3}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-x }
& = & 14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 14 \color{blue}{+3} \\\Leftrightarrow &-11x
& = &17\\\Leftrightarrow & \color{red}{-11}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+9}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9-11x }
& = & 9 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & 9x \color{blue}{-11x }
& = & 9 \color{blue}{-9} \\\Leftrightarrow &-2x
& = &0\\\Leftrightarrow & \color{red}{-2}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}}
& = & \frac{0}{-2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-3}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3-9x }
& = & 12 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & -4x \color{blue}{-9x }
& = & 12 \color{blue}{+3} \\\Leftrightarrow &-13x
& = &15\\\Leftrightarrow & \color{red}{-13}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+3}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-x }
& = & -7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -7 \color{blue}{-3} \\\Leftrightarrow &-15x
& = &-10\\\Leftrightarrow & \color{red}{-15}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-x }
& = & 2 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 2 \color{blue}{-1} \\\Leftrightarrow &-13x
& = &1\\\Leftrightarrow & \color{red}{-13}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-2}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2+11x }
& = & 11 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 9x \color{blue}{+11x }
& = & 11 \color{blue}{+2} \\\Leftrightarrow &20x
& = &13\\\Leftrightarrow & \color{red}{20}x
& = &13\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{13}{20} \\\Leftrightarrow & \color{green}{ x = \frac{13}{20} } & & \\ & V = \left\{ \frac{13}{20} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-1}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1-9x }
& = & 4 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & x \color{blue}{-9x }
& = & 4 \color{blue}{+1} \\\Leftrightarrow &-8x
& = &5\\\Leftrightarrow & \color{red}{-8}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-12}& = & -10 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12-12x }
& = & -10 \color{red}{ +12x }\color{blue}{+12-12x } \\\Leftrightarrow & x \color{blue}{-12x }
& = & -10 \color{blue}{+12} \\\Leftrightarrow &-11x
& = &2\\\Leftrightarrow & \color{red}{-11}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)