Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(10x+15=-14+x\)
- \(-14x-11=8+x\)
- \(8x-9=10-15x\)
- \(-14x+2=4+x\)
- \(11x+11=14+12x\)
- \(-10x-13=-3+7x\)
- \(x+1=-7-12x\)
- \(-2x-5=5+x\)
- \(-9x+11=-12+7x\)
- \(2x+7=2+5x\)
- \(3x+9=2+4x\)
- \(-12x-6=13+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 10x \color{red}{+15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15-x }
& = & -14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 10x \color{blue}{-x }
& = & -14 \color{blue}{-15} \\\Leftrightarrow &9x
& = &-29\\\Leftrightarrow & \color{red}{9}x
& = &-29\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-29}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{9} } & & \\ & V = \left\{ \frac{-29}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-11}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-x }
& = & 8 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 8 \color{blue}{+11} \\\Leftrightarrow &-15x
& = &19\\\Leftrightarrow & \color{red}{-15}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{15} } & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-9}& = & 10 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9+15x }
& = & 10 \color{red}{ -15x }\color{blue}{+9+15x } \\\Leftrightarrow & 8x \color{blue}{+15x }
& = & 10 \color{blue}{+9} \\\Leftrightarrow &23x
& = &19\\\Leftrightarrow & \color{red}{23}x
& = &19\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{19}{23} \\\Leftrightarrow & \color{green}{ x = \frac{19}{23} } & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x }
& = & 4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 4 \color{blue}{-2} \\\Leftrightarrow &-15x
& = &2\\\Leftrightarrow & \color{red}{-15}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+11}& = & 14 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11-12x }
& = & 14 \color{red}{ +12x }\color{blue}{-11-12x } \\\Leftrightarrow & 11x \color{blue}{-12x }
& = & 14 \color{blue}{-11} \\\Leftrightarrow &-x
& = &3\\\Leftrightarrow & \color{red}{-}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-13}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-7x }
& = & -3 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & -10x \color{blue}{-7x }
& = & -3 \color{blue}{+13} \\\Leftrightarrow &-17x
& = &10\\\Leftrightarrow & \color{red}{-17}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+1}& = & -7 \color{red}{ -12x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1+12x }
& = & -7 \color{red}{ -12x }\color{blue}{-1+12x } \\\Leftrightarrow & x \color{blue}{+12x }
& = & -7 \color{blue}{-1} \\\Leftrightarrow &13x
& = &-8\\\Leftrightarrow & \color{red}{13}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-5}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5-x }
& = & 5 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & 5 \color{blue}{+5} \\\Leftrightarrow &-3x
& = &10\\\Leftrightarrow & \color{red}{-3}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+11}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-7x }
& = & -12 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -9x \color{blue}{-7x }
& = & -12 \color{blue}{-11} \\\Leftrightarrow &-16x
& = &-23\\\Leftrightarrow & \color{red}{-16}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-23}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{23}{16} } & & \\ & V = \left\{ \frac{23}{16} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+7}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-5x }
& = & 2 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & 2x \color{blue}{-5x }
& = & 2 \color{blue}{-7} \\\Leftrightarrow &-3x
& = &-5\\\Leftrightarrow & \color{red}{-3}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+9}& = & 2 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9-4x }
& = & 2 \color{red}{ +4x }\color{blue}{-9-4x } \\\Leftrightarrow & 3x \color{blue}{-4x }
& = & 2 \color{blue}{-9} \\\Leftrightarrow &-x
& = &-7\\\Leftrightarrow & \color{red}{-}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-x }
& = & 13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 13 \color{blue}{+6} \\\Leftrightarrow &-13x
& = &19\\\Leftrightarrow & \color{red}{-13}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)