Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-10x+9=-1+x\)
- \(4x+14=-2+3x\)
- \(7x-4=3+5x\)
- \(-11x-14=15+x\)
- \(-5x-7=15+x\)
- \(13x-3=-7-12x\)
- \(7x-4=13+x\)
- \(6x+9=-6-11x\)
- \(13x-1=-4+3x\)
- \(-11x-11=14+9x\)
- \(-x+14=-15-9x\)
- \(-13x+5=-8+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -10x \color{red}{+9}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-x }
& = & -1 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -1 \color{blue}{-9} \\\Leftrightarrow &-11x
& = &-10\\\Leftrightarrow & \color{red}{-11}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+14}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14-3x }
& = & -2 \color{red}{ +3x }\color{blue}{-14-3x } \\\Leftrightarrow & 4x \color{blue}{-3x }
& = & -2 \color{blue}{-14} \\\Leftrightarrow &x
& = &-16\\\Leftrightarrow & \color{red}{}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -16 \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-4}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4-5x }
& = & 3 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & 7x \color{blue}{-5x }
& = & 3 \color{blue}{+4} \\\Leftrightarrow &2x
& = &7\\\Leftrightarrow & \color{red}{2}x
& = &7\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{7}{2} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-14}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-x }
& = & 15 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 15 \color{blue}{+14} \\\Leftrightarrow &-12x
& = &29\\\Leftrightarrow & \color{red}{-12}x
& = &29\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{29}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{12} } & & \\ & V = \left\{ \frac{-29}{12} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-7}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-7}\color{blue}{+7-x }
& = & 15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 15 \color{blue}{+7} \\\Leftrightarrow &-6x
& = &22\\\Leftrightarrow & \color{red}{-6}x
& = &22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-3}& = & -7 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+12x }
& = & -7 \color{red}{ -12x }\color{blue}{+3+12x } \\\Leftrightarrow & 13x \color{blue}{+12x }
& = & -7 \color{blue}{+3} \\\Leftrightarrow &25x
& = &-4\\\Leftrightarrow & \color{red}{25}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{-4}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{25} } & & \\ & V = \left\{ \frac{-4}{25} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-4}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4-x }
& = & 13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 7x \color{blue}{-x }
& = & 13 \color{blue}{+4} \\\Leftrightarrow &6x
& = &17\\\Leftrightarrow & \color{red}{6}x
& = &17\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}}
& = & \frac{17}{6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+9}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9+11x }
& = & -6 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & -6 \color{blue}{-9} \\\Leftrightarrow &17x
& = &-15\\\Leftrightarrow & \color{red}{17}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-15}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{17} } & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-1}& = & -4 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1-3x }
& = & -4 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & 13x \color{blue}{-3x }
& = & -4 \color{blue}{+1} \\\Leftrightarrow &10x
& = &-3\\\Leftrightarrow & \color{red}{10}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{-3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-11}& = & 14 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-9x }
& = & 14 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & -11x \color{blue}{-9x }
& = & 14 \color{blue}{+11} \\\Leftrightarrow &-20x
& = &25\\\Leftrightarrow & \color{red}{-20}x
& = &25\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{25}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+14}& = & -15 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14+9x }
& = & -15 \color{red}{ -9x }\color{blue}{-14+9x } \\\Leftrightarrow & -x \color{blue}{+9x }
& = & -15 \color{blue}{-14} \\\Leftrightarrow &8x
& = &-29\\\Leftrightarrow & \color{red}{8}x
& = &-29\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{-29}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{8} } & & \\ & V = \left\{ \frac{-29}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+5}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5-x }
& = & -8 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -8 \color{blue}{-5} \\\Leftrightarrow &-14x
& = &-13\\\Leftrightarrow & \color{red}{-14}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-13}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)