Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-2x-7=10+11x\)
- \(4x+14=-2+11x\)
- \(-12x+3=10+13x\)
- \(-4x+15=5+x\)
- \(-x-7=11-14x\)
- \(7x+9=-2-13x\)
- \(3x-9=-3+x\)
- \(-3x-15=9+x\)
- \(5x+2=-4-7x\)
- \(11x+6=-13+x\)
- \(-8x+11=3+9x\)
- \(-15x+1=-9+4x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -2x \color{red}{-7}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-11x }
& = & 10 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & -2x \color{blue}{-11x }
& = & 10 \color{blue}{+7} \\\Leftrightarrow &-13x
& = &17\\\Leftrightarrow & \color{red}{-13}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+14}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14-11x }
& = & -2 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & 4x \color{blue}{-11x }
& = & -2 \color{blue}{-14} \\\Leftrightarrow &-7x
& = &-16\\\Leftrightarrow & \color{red}{-7}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+3}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-13x }
& = & 10 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & 10 \color{blue}{-3} \\\Leftrightarrow &-25x
& = &7\\\Leftrightarrow & \color{red}{-25}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{7}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{25} } & & \\ & V = \left\{ \frac{-7}{25} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+15}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-x }
& = & 5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & 5 \color{blue}{-15} \\\Leftrightarrow &-5x
& = &-10\\\Leftrightarrow & \color{red}{-5}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-7}& = & 11 \color{red}{ -14x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7+14x }
& = & 11 \color{red}{ -14x }\color{blue}{+7+14x } \\\Leftrightarrow & -x \color{blue}{+14x }
& = & 11 \color{blue}{+7} \\\Leftrightarrow &13x
& = &18\\\Leftrightarrow & \color{red}{13}x
& = &18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+9}& = & -2 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9+13x }
& = & -2 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 7x \color{blue}{+13x }
& = & -2 \color{blue}{-9} \\\Leftrightarrow &20x
& = &-11\\\Leftrightarrow & \color{red}{20}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{-11}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{20} } & & \\ & V = \left\{ \frac{-11}{20} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-9}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-9}\color{blue}{+9-x }
& = & -3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 3x \color{blue}{-x }
& = & -3 \color{blue}{+9} \\\Leftrightarrow &2x
& = &6\\\Leftrightarrow & \color{red}{2}x
& = &6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{6}{2} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-15}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15-x }
& = & 9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 9 \color{blue}{+15} \\\Leftrightarrow &-4x
& = &24\\\Leftrightarrow & \color{red}{-4}x
& = &24\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{24}{-4} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+2}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2+7x }
& = & -4 \color{red}{ -7x }\color{blue}{-2+7x } \\\Leftrightarrow & 5x \color{blue}{+7x }
& = & -4 \color{blue}{-2} \\\Leftrightarrow &12x
& = &-6\\\Leftrightarrow & \color{red}{12}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}}
& = & \frac{-6}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+6}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6-x }
& = & -13 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 11x \color{blue}{-x }
& = & -13 \color{blue}{-6} \\\Leftrightarrow &10x
& = &-19\\\Leftrightarrow & \color{red}{10}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{-19}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{10} } & & \\ & V = \left\{ \frac{-19}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+11}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-9x }
& = & 3 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & -8x \color{blue}{-9x }
& = & 3 \color{blue}{-11} \\\Leftrightarrow &-17x
& = &-8\\\Leftrightarrow & \color{red}{-17}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+1}& = & -9 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-4x }
& = & -9 \color{red}{ +4x }\color{blue}{-1-4x } \\\Leftrightarrow & -15x \color{blue}{-4x }
& = & -9 \color{blue}{-1} \\\Leftrightarrow &-19x
& = &-10\\\Leftrightarrow & \color{red}{-19}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-10}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)