Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(5x+15=-5+2x\)
- \(5x+9=-5+4x\)
- \(-11x-12=6+9x\)
- \(-9x+7=-7+x\)
- \(-7x-6=-11+x\)
- \(-9x+9=-7+x\)
- \(-5x+15=7+x\)
- \(5x+12=1+12x\)
- \(3x-7=11+5x\)
- \(12x-8=-8-11x\)
- \(-11x-6=9+x\)
- \(15x+3=10+7x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 5x \color{red}{+15}& = & -5 \color{red}{ +2x } \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15-2x }
& = & -5 \color{red}{ +2x }\color{blue}{-15-2x } \\\Leftrightarrow & 5x \color{blue}{-2x }
& = & -5 \color{blue}{-15} \\\Leftrightarrow &3x
& = &-20\\\Leftrightarrow & \color{red}{3}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{-20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+9}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{+9}\color{blue}{-9-4x }
& = & -5 \color{red}{ +4x }\color{blue}{-9-4x } \\\Leftrightarrow & 5x \color{blue}{-4x }
& = & -5 \color{blue}{-9} \\\Leftrightarrow &x
& = &-14\\\Leftrightarrow & \color{red}{}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -14 \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-12}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12-9x }
& = & 6 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & -11x \color{blue}{-9x }
& = & 6 \color{blue}{+12} \\\Leftrightarrow &-20x
& = &18\\\Leftrightarrow & \color{red}{-20}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{18}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-x }
& = & -7 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -7 \color{blue}{-7} \\\Leftrightarrow &-10x
& = &-14\\\Leftrightarrow & \color{red}{-10}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-6}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-x }
& = & -11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -11 \color{blue}{+6} \\\Leftrightarrow &-8x
& = &-5\\\Leftrightarrow & \color{red}{-8}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-x }
& = & -7 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -7 \color{blue}{-9} \\\Leftrightarrow &-10x
& = &-16\\\Leftrightarrow & \color{red}{-10}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+15}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15-x }
& = & 7 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 7 \color{blue}{-15} \\\Leftrightarrow &-6x
& = &-8\\\Leftrightarrow & \color{red}{-6}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+12}& = & 1 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12-12x }
& = & 1 \color{red}{ +12x }\color{blue}{-12-12x } \\\Leftrightarrow & 5x \color{blue}{-12x }
& = & 1 \color{blue}{-12} \\\Leftrightarrow &-7x
& = &-11\\\Leftrightarrow & \color{red}{-7}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-7}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7-5x }
& = & 11 \color{red}{ +5x }\color{blue}{+7-5x } \\\Leftrightarrow & 3x \color{blue}{-5x }
& = & 11 \color{blue}{+7} \\\Leftrightarrow &-2x
& = &18\\\Leftrightarrow & \color{red}{-2}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}}
& = & \frac{18}{-2} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-8}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8+11x }
& = & -8 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & -8 \color{blue}{+8} \\\Leftrightarrow &23x
& = &0\\\Leftrightarrow & \color{red}{23}x
& = &0\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{0}{23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-x }
& = & 9 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 9 \color{blue}{+6} \\\Leftrightarrow &-12x
& = &15\\\Leftrightarrow & \color{red}{-12}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+3}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3-7x }
& = & 10 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & 15x \color{blue}{-7x }
& = & 10 \color{blue}{-3} \\\Leftrightarrow &8x
& = &7\\\Leftrightarrow & \color{red}{8}x
& = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)