Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-12x-2=8+x\)
- \(15x+1=-2+7x\)
- \(11x+14=15+10x\)
- \(6x+1=-12+11x\)
- \(-10x-2=3+x\)
- \(3x-2=-3+x\)
- \(-14x+4=5+x\)
- \(x-1=-15-14x\)
- \(4x+11=-9+13x\)
- \(14x-2=-1-13x\)
- \(-2x-2=8+x\)
- \(-15x+10=-1+8x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -12x \color{red}{-2}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-2}\color{blue}{+2-x }
& = & 8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 8 \color{blue}{+2} \\\Leftrightarrow &-13x
& = &10\\\Leftrightarrow & \color{red}{-13}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+1}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1-7x }
& = & -2 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 15x \color{blue}{-7x }
& = & -2 \color{blue}{-1} \\\Leftrightarrow &8x
& = &-3\\\Leftrightarrow & \color{red}{8}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{-3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+14}& = & 15 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14-10x }
& = & 15 \color{red}{ +10x }\color{blue}{-14-10x } \\\Leftrightarrow & 11x \color{blue}{-10x }
& = & 15 \color{blue}{-14} \\\Leftrightarrow &x
& = &1\\\Leftrightarrow & \color{red}{}x
& = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+1}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1-11x }
& = & -12 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & 6x \color{blue}{-11x }
& = & -12 \color{blue}{-1} \\\Leftrightarrow &-5x
& = &-13\\\Leftrightarrow & \color{red}{-5}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-2}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-x }
& = & 3 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 3 \color{blue}{+2} \\\Leftrightarrow &-11x
& = &5\\\Leftrightarrow & \color{red}{-11}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2-x }
& = & -3 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 3x \color{blue}{-x }
& = & -3 \color{blue}{+2} \\\Leftrightarrow &2x
& = &-1\\\Leftrightarrow & \color{red}{2}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{-1}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x }
& = & 5 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 5 \color{blue}{-4} \\\Leftrightarrow &-15x
& = &1\\\Leftrightarrow & \color{red}{-15}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-1}& = & -15 \color{red}{ -14x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1+14x }
& = & -15 \color{red}{ -14x }\color{blue}{+1+14x } \\\Leftrightarrow & x \color{blue}{+14x }
& = & -15 \color{blue}{+1} \\\Leftrightarrow &15x
& = &-14\\\Leftrightarrow & \color{red}{15}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{-14}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+11}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11-13x }
& = & -9 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & 4x \color{blue}{-13x }
& = & -9 \color{blue}{-11} \\\Leftrightarrow &-9x
& = &-20\\\Leftrightarrow & \color{red}{-9}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{20}{9} } & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-2}& = & -1 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2+13x }
& = & -1 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 14x \color{blue}{+13x }
& = & -1 \color{blue}{+2} \\\Leftrightarrow &27x
& = &1\\\Leftrightarrow & \color{red}{27}x
& = &1\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}}
& = & \frac{1}{27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{27} } & & \\ & V = \left\{ \frac{1}{27} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-2}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2-x }
& = & 8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & 8 \color{blue}{+2} \\\Leftrightarrow &-3x
& = &10\\\Leftrightarrow & \color{red}{-3}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+10}& = & -1 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-8x }
& = & -1 \color{red}{ +8x }\color{blue}{-10-8x } \\\Leftrightarrow & -15x \color{blue}{-8x }
& = & -1 \color{blue}{-10} \\\Leftrightarrow &-23x
& = &-11\\\Leftrightarrow & \color{red}{-23}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{-11}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{11}{23} } & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)