Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(12x-3=1+5x\)
- \(10x+14=-8-3x\)
- \(9x-9=13-13x\)
- \(-15x-15=9+13x\)
- \(13x+14=15+x\)
- \(x+14=1+10x\)
- \(5x+6=15+4x\)
- \(9x-9=6+13x\)
- \(-10x-4=7+x\)
- \(11x+13=-5-5x\)
- \(14x+15=-13-13x\)
- \(-9x-10=12+7x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 12x \color{red}{-3}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-5x }
& = & 1 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & 12x \color{blue}{-5x }
& = & 1 \color{blue}{+3} \\\Leftrightarrow &7x
& = &4\\\Leftrightarrow & \color{red}{7}x
& = &4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+14}& = & -8 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14+3x }
& = & -8 \color{red}{ -3x }\color{blue}{-14+3x } \\\Leftrightarrow & 10x \color{blue}{+3x }
& = & -8 \color{blue}{-14} \\\Leftrightarrow &13x
& = &-22\\\Leftrightarrow & \color{red}{13}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{13} } & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-9}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9+13x }
& = & 13 \color{red}{ -13x }\color{blue}{+9+13x } \\\Leftrightarrow & 9x \color{blue}{+13x }
& = & 13 \color{blue}{+9} \\\Leftrightarrow &22x
& = &22\\\Leftrightarrow & \color{red}{22}x
& = &22\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}}
& = & \frac{22}{22} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-15}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-13x }
& = & 9 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & 9 \color{blue}{+15} \\\Leftrightarrow &-28x
& = &24\\\Leftrightarrow & \color{red}{-28}x
& = &24\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{24}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+14}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14-x }
& = & 15 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 13x \color{blue}{-x }
& = & 15 \color{blue}{-14} \\\Leftrightarrow &12x
& = &1\\\Leftrightarrow & \color{red}{12}x
& = &1\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}}
& = & \frac{1}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+14}& = & 1 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14-10x }
& = & 1 \color{red}{ +10x }\color{blue}{-14-10x } \\\Leftrightarrow & x \color{blue}{-10x }
& = & 1 \color{blue}{-14} \\\Leftrightarrow &-9x
& = &-13\\\Leftrightarrow & \color{red}{-9}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+6}& = & 15 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6-4x }
& = & 15 \color{red}{ +4x }\color{blue}{-6-4x } \\\Leftrightarrow & 5x \color{blue}{-4x }
& = & 15 \color{blue}{-6} \\\Leftrightarrow &x
& = &9\\\Leftrightarrow & \color{red}{}x
& = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-9}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9-13x }
& = & 6 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 9x \color{blue}{-13x }
& = & 6 \color{blue}{+9} \\\Leftrightarrow &-4x
& = &15\\\Leftrightarrow & \color{red}{-4}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{15}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{4} } & & \\ & V = \left\{ \frac{-15}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-4}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x }
& = & 7 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 7 \color{blue}{+4} \\\Leftrightarrow &-11x
& = &11\\\Leftrightarrow & \color{red}{-11}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{11}{-11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+13}& = & -5 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13+5x }
& = & -5 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & 11x \color{blue}{+5x }
& = & -5 \color{blue}{-13} \\\Leftrightarrow &16x
& = &-18\\\Leftrightarrow & \color{red}{16}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}}
& = & \frac{-18}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+15}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15+13x }
& = & -13 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 14x \color{blue}{+13x }
& = & -13 \color{blue}{-15} \\\Leftrightarrow &27x
& = &-28\\\Leftrightarrow & \color{red}{27}x
& = &-28\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}}
& = & \frac{-28}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{27} } & & \\ & V = \left\{ \frac{-28}{27} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-10}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-7x }
& = & 12 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & -9x \color{blue}{-7x }
& = & 12 \color{blue}{+10} \\\Leftrightarrow &-16x
& = &22\\\Leftrightarrow & \color{red}{-16}x
& = &22\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{22}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)