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