Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(7x-7=3-6x\)
- \(-7x-5=-13+x\)
- \(-12x+10=1+x\)
- \(-2x-4=-15+x\)
- \(-x-12=-7+12x\)
- \(4x-9=8+7x\)
- \(-12x-1=9+13x\)
- \(8x+4=2-7x\)
- \(14x-3=6-11x\)
- \(-4x+15=15+9x\)
- \(-7x+9=-10+x\)
- \(3x+14=14-2x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 7x \color{red}{-7}& = & 3 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7+6x }
& = & 3 \color{red}{ -6x }\color{blue}{+7+6x } \\\Leftrightarrow & 7x \color{blue}{+6x }
& = & 3 \color{blue}{+7} \\\Leftrightarrow &13x
& = &10\\\Leftrightarrow & \color{red}{13}x
& = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-5}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-x }
& = & -13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -13 \color{blue}{+5} \\\Leftrightarrow &-8x
& = &-8\\\Leftrightarrow & \color{red}{-8}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-8}{-8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10-x }
& = & 1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 1 \color{blue}{-10} \\\Leftrightarrow &-13x
& = &-9\\\Leftrightarrow & \color{red}{-13}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-4}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-x }
& = & -15 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & -15 \color{blue}{+4} \\\Leftrightarrow &-3x
& = &-11\\\Leftrightarrow & \color{red}{-3}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-12}& = & -7 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12-12x }
& = & -7 \color{red}{ +12x }\color{blue}{+12-12x } \\\Leftrightarrow & -x \color{blue}{-12x }
& = & -7 \color{blue}{+12} \\\Leftrightarrow &-13x
& = &5\\\Leftrightarrow & \color{red}{-13}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-9}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9-7x }
& = & 8 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & 4x \color{blue}{-7x }
& = & 8 \color{blue}{+9} \\\Leftrightarrow &-3x
& = &17\\\Leftrightarrow & \color{red}{-3}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{3} } & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-1}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-13x }
& = & 9 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & 9 \color{blue}{+1} \\\Leftrightarrow &-25x
& = &10\\\Leftrightarrow & \color{red}{-25}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{10}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+4}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4+7x }
& = & 2 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 8x \color{blue}{+7x }
& = & 2 \color{blue}{-4} \\\Leftrightarrow &15x
& = &-2\\\Leftrightarrow & \color{red}{15}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{-2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-3}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3+11x }
& = & 6 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 14x \color{blue}{+11x }
& = & 6 \color{blue}{+3} \\\Leftrightarrow &25x
& = &9\\\Leftrightarrow & \color{red}{25}x
& = &9\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{9}{25} \\\Leftrightarrow & \color{green}{ x = \frac{9}{25} } & & \\ & V = \left\{ \frac{9}{25} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+15}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-9x }
& = & 15 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & -4x \color{blue}{-9x }
& = & 15 \color{blue}{-15} \\\Leftrightarrow &-13x
& = &0\\\Leftrightarrow & \color{red}{-13}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x }
& = & -10 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -10 \color{blue}{-9} \\\Leftrightarrow &-8x
& = &-19\\\Leftrightarrow & \color{red}{-8}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{19}{8} } & & \\ & V = \left\{ \frac{19}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+14}& = & 14 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14+2x }
& = & 14 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 3x \color{blue}{+2x }
& = & 14 \color{blue}{-14} \\\Leftrightarrow &5x
& = &0\\\Leftrightarrow & \color{red}{5}x
& = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)