Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(10x-7=1-3x\)
- \(6x+3=-9+5x\)
- \(-14x+10=-3+3x\)
- \(-8x-4=-3+3x\)
- \(-7x-10=10+x\)
- \(-12x-10=-9+x\)
- \(9x-5=-6-11x\)
- \(-6x+13=-13+x\)
- \(15x-5=-3-2x\)
- \(-14x+3=11+x\)
- \(-13x-12=12+x\)
- \(13x-15=-1+9x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 10x \color{red}{-7}& = & 1 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7+3x }
& = & 1 \color{red}{ -3x }\color{blue}{+7+3x } \\\Leftrightarrow & 10x \color{blue}{+3x }
& = & 1 \color{blue}{+7} \\\Leftrightarrow &13x
& = &8\\\Leftrightarrow & \color{red}{13}x
& = &8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+3}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3-5x }
& = & -9 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 6x \color{blue}{-5x }
& = & -9 \color{blue}{-3} \\\Leftrightarrow &x
& = &-12\\\Leftrightarrow & \color{red}{}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+10}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-3x }
& = & -3 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & -14x \color{blue}{-3x }
& = & -3 \color{blue}{-10} \\\Leftrightarrow &-17x
& = &-13\\\Leftrightarrow & \color{red}{-17}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-13}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-4}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-3x }
& = & -3 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & -8x \color{blue}{-3x }
& = & -3 \color{blue}{+4} \\\Leftrightarrow &-11x
& = &1\\\Leftrightarrow & \color{red}{-11}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-10}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-x }
& = & 10 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & 10 \color{blue}{+10} \\\Leftrightarrow &-8x
& = &20\\\Leftrightarrow & \color{red}{-8}x
& = &20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-x }
& = & -9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -9 \color{blue}{+10} \\\Leftrightarrow &-13x
& = &1\\\Leftrightarrow & \color{red}{-13}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-5}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5+11x }
& = & -6 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 9x \color{blue}{+11x }
& = & -6 \color{blue}{+5} \\\Leftrightarrow &20x
& = &-1\\\Leftrightarrow & \color{red}{20}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{-1}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{20} } & & \\ & V = \left\{ \frac{-1}{20} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+13}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-x }
& = & -13 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -13 \color{blue}{-13} \\\Leftrightarrow &-7x
& = &-26\\\Leftrightarrow & \color{red}{-7}x
& = &-26\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-26}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{26}{7} } & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-5}& = & -3 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5+2x }
& = & -3 \color{red}{ -2x }\color{blue}{+5+2x } \\\Leftrightarrow & 15x \color{blue}{+2x }
& = & -3 \color{blue}{+5} \\\Leftrightarrow &17x
& = &2\\\Leftrightarrow & \color{red}{17}x
& = &2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+3}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-x }
& = & 11 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 11 \color{blue}{-3} \\\Leftrightarrow &-15x
& = &8\\\Leftrightarrow & \color{red}{-15}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-x }
& = & 12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 12 \color{blue}{+12} \\\Leftrightarrow &-14x
& = &24\\\Leftrightarrow & \color{red}{-14}x
& = &24\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{24}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-15}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15-9x }
& = & -1 \color{red}{ +9x }\color{blue}{+15-9x } \\\Leftrightarrow & 13x \color{blue}{-9x }
& = & -1 \color{blue}{+15} \\\Leftrightarrow &4x
& = &14\\\Leftrightarrow & \color{red}{4}x
& = &14\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{14}{4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)