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