Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(2x-11=11+x\)
- \(10x+5=-9+x\)
- \(-11x+7=4+12x\)
- \(-13x+14=3+9x\)
- \(x-3=5-8x\)
- \(-4x-1=2+x\)
- \(14x+3=14+5x\)
- \(-7x-14=-4+x\)
- \(4x-4=-8-7x\)
- \(6x-2=9-11x\)
- \(12x+9=-10-7x\)
- \(13x-11=15-12x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 2x \color{red}{-11}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-x }
& = & 11 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & 11 \color{blue}{+11} \\\Leftrightarrow &x
& = &22\\\Leftrightarrow & \color{red}{}x
& = &22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 22 \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5-x }
& = & -9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 10x \color{blue}{-x }
& = & -9 \color{blue}{-5} \\\Leftrightarrow &9x
& = &-14\\\Leftrightarrow & \color{red}{9}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-14}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+7}& = & 4 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-12x }
& = & 4 \color{red}{ +12x }\color{blue}{-7-12x } \\\Leftrightarrow & -11x \color{blue}{-12x }
& = & 4 \color{blue}{-7} \\\Leftrightarrow &-23x
& = &-3\\\Leftrightarrow & \color{red}{-23}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{-3}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{3}{23} } & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+14}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-9x }
& = & 3 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & -13x \color{blue}{-9x }
& = & 3 \color{blue}{-14} \\\Leftrightarrow &-22x
& = &-11\\\Leftrightarrow & \color{red}{-22}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}}
& = & \frac{-11}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-3}& = & 5 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3+8x }
& = & 5 \color{red}{ -8x }\color{blue}{+3+8x } \\\Leftrightarrow & x \color{blue}{+8x }
& = & 5 \color{blue}{+3} \\\Leftrightarrow &9x
& = &8\\\Leftrightarrow & \color{red}{9}x
& = &8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1-x }
& = & 2 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & 2 \color{blue}{+1} \\\Leftrightarrow &-5x
& = &3\\\Leftrightarrow & \color{red}{-5}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+3}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3-5x }
& = & 14 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 14x \color{blue}{-5x }
& = & 14 \color{blue}{-3} \\\Leftrightarrow &9x
& = &11\\\Leftrightarrow & \color{red}{9}x
& = &11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-14}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-x }
& = & -4 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -4 \color{blue}{+14} \\\Leftrightarrow &-8x
& = &10\\\Leftrightarrow & \color{red}{-8}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-4}& = & -8 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4+7x }
& = & -8 \color{red}{ -7x }\color{blue}{+4+7x } \\\Leftrightarrow & 4x \color{blue}{+7x }
& = & -8 \color{blue}{+4} \\\Leftrightarrow &11x
& = &-4\\\Leftrightarrow & \color{red}{11}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-2}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2+11x }
& = & 9 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & 9 \color{blue}{+2} \\\Leftrightarrow &17x
& = &11\\\Leftrightarrow & \color{red}{17}x
& = &11\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{11}{17} \\\Leftrightarrow & \color{green}{ x = \frac{11}{17} } & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+9}& = & -10 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9+7x }
& = & -10 \color{red}{ -7x }\color{blue}{-9+7x } \\\Leftrightarrow & 12x \color{blue}{+7x }
& = & -10 \color{blue}{-9} \\\Leftrightarrow &19x
& = &-19\\\Leftrightarrow & \color{red}{19}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-19}{19} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-11}& = & 15 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11+12x }
& = & 15 \color{red}{ -12x }\color{blue}{+11+12x } \\\Leftrightarrow & 13x \color{blue}{+12x }
& = & 15 \color{blue}{+11} \\\Leftrightarrow &25x
& = &26\\\Leftrightarrow & \color{red}{25}x
& = &26\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{26}{25} \\\Leftrightarrow & \color{green}{ x = \frac{26}{25} } & & \\ & V = \left\{ \frac{26}{25} \right\} & \\\end{align}\)