Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-10x-2=-12+11x\)
- \(2x-3=-2+x\)
- \(-2x-14=-5+x\)
- \(x-11=4-4x\)
- \(-11x-14=4+12x\)
- \(2x+13=-2+x\)
- \(6x-13=12+11x\)
- \(5x-13=-15-4x\)
- \(-7x+3=-10+x\)
- \(-10x-13=-12+11x\)
- \(5x-8=-6+x\)
- \(9x+11=13+7x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -10x \color{red}{-2}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-11x }
& = & -12 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & -10x \color{blue}{-11x }
& = & -12 \color{blue}{+2} \\\Leftrightarrow &-21x
& = &-10\\\Leftrightarrow & \color{red}{-21}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}}
& = & \frac{-10}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{10}{21} } & & \\ & V = \left\{ \frac{10}{21} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-3}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-x }
& = & -2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & -2 \color{blue}{+3} \\\Leftrightarrow &x
& = &1\\\Leftrightarrow & \color{red}{}x
& = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-14}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14-x }
& = & -5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & -5 \color{blue}{+14} \\\Leftrightarrow &-3x
& = &9\\\Leftrightarrow & \color{red}{-3}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-11}& = & 4 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11+4x }
& = & 4 \color{red}{ -4x }\color{blue}{+11+4x } \\\Leftrightarrow & x \color{blue}{+4x }
& = & 4 \color{blue}{+11} \\\Leftrightarrow &5x
& = &15\\\Leftrightarrow & \color{red}{5}x
& = &15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{15}{5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-14}& = & 4 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-12x }
& = & 4 \color{red}{ +12x }\color{blue}{+14-12x } \\\Leftrightarrow & -11x \color{blue}{-12x }
& = & 4 \color{blue}{+14} \\\Leftrightarrow &-23x
& = &18\\\Leftrightarrow & \color{red}{-23}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{18}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{23} } & & \\ & V = \left\{ \frac{-18}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+13}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-x }
& = & -2 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & -2 \color{blue}{-13} \\\Leftrightarrow &x
& = &-15\\\Leftrightarrow & \color{red}{}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -15 \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-13}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13-11x }
& = & 12 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 6x \color{blue}{-11x }
& = & 12 \color{blue}{+13} \\\Leftrightarrow &-5x
& = &25\\\Leftrightarrow & \color{red}{-5}x
& = &25\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{25}{-5} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-13}& = & -15 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13+4x }
& = & -15 \color{red}{ -4x }\color{blue}{+13+4x } \\\Leftrightarrow & 5x \color{blue}{+4x }
& = & -15 \color{blue}{+13} \\\Leftrightarrow &9x
& = &-2\\\Leftrightarrow & \color{red}{9}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-x }
& = & -10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -10 \color{blue}{-3} \\\Leftrightarrow &-8x
& = &-13\\\Leftrightarrow & \color{red}{-8}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{8} } & & \\ & V = \left\{ \frac{13}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-13}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-11x }
& = & -12 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & -10x \color{blue}{-11x }
& = & -12 \color{blue}{+13} \\\Leftrightarrow &-21x
& = &1\\\Leftrightarrow & \color{red}{-21}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}}
& = & \frac{1}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{21} } & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-8}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8-x }
& = & -6 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 5x \color{blue}{-x }
& = & -6 \color{blue}{+8} \\\Leftrightarrow &4x
& = &2\\\Leftrightarrow & \color{red}{4}x
& = &2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+11}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{+11}\color{blue}{-11-7x }
& = & 13 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & 9x \color{blue}{-7x }
& = & 13 \color{blue}{-11} \\\Leftrightarrow &2x
& = &2\\\Leftrightarrow & \color{red}{2}x
& = &2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{2}{2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)