Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-5x-11=9+x\)
- \(3x+11=-14-11x\)
- \(3x+9=2-2x\)
- \(4x+10=-4+x\)
- \(-6x-7=15+x\)
- \(12x+12=7+x\)
- \(-4x-5=-2+x\)
- \(-10x-2=-11+11x\)
- \(-5x+12=-13+x\)
- \(4x+2=9-11x\)
- \(13x-8=-15-4x\)
- \(-8x+7=6+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -5x \color{red}{-11}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-x }
& = & 9 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 9 \color{blue}{+11} \\\Leftrightarrow &-6x
& = &20\\\Leftrightarrow & \color{red}{-6}x
& = &20\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{20}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+11}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11+11x }
& = & -14 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 3x \color{blue}{+11x }
& = & -14 \color{blue}{-11} \\\Leftrightarrow &14x
& = &-25\\\Leftrightarrow & \color{red}{14}x
& = &-25\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{-25}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{14} } & & \\ & V = \left\{ \frac{-25}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+9}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9+2x }
& = & 2 \color{red}{ -2x }\color{blue}{-9+2x } \\\Leftrightarrow & 3x \color{blue}{+2x }
& = & 2 \color{blue}{-9} \\\Leftrightarrow &5x
& = &-7\\\Leftrightarrow & \color{red}{5}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+10}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10-x }
& = & -4 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 4x \color{blue}{-x }
& = & -4 \color{blue}{-10} \\\Leftrightarrow &3x
& = &-14\\\Leftrightarrow & \color{red}{3}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{-14}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-7}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-x }
& = & 15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & 15 \color{blue}{+7} \\\Leftrightarrow &-7x
& = &22\\\Leftrightarrow & \color{red}{-7}x
& = &22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12-x }
& = & 7 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & 7 \color{blue}{-12} \\\Leftrightarrow &11x
& = &-5\\\Leftrightarrow & \color{red}{11}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-5}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-x }
& = & -2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -2 \color{blue}{+5} \\\Leftrightarrow &-5x
& = &3\\\Leftrightarrow & \color{red}{-5}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-2}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-11x }
& = & -11 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & -10x \color{blue}{-11x }
& = & -11 \color{blue}{+2} \\\Leftrightarrow &-21x
& = &-9\\\Leftrightarrow & \color{red}{-21}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}}
& = & \frac{-9}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+12}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-x }
& = & -13 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & -13 \color{blue}{-12} \\\Leftrightarrow &-6x
& = &-25\\\Leftrightarrow & \color{red}{-6}x
& = &-25\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-25}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{25}{6} } & & \\ & V = \left\{ \frac{25}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+2}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2+11x }
& = & 9 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 4x \color{blue}{+11x }
& = & 9 \color{blue}{-2} \\\Leftrightarrow &15x
& = &7\\\Leftrightarrow & \color{red}{15}x
& = &7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-8}& = & -15 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8+4x }
& = & -15 \color{red}{ -4x }\color{blue}{+8+4x } \\\Leftrightarrow & 13x \color{blue}{+4x }
& = & -15 \color{blue}{+8} \\\Leftrightarrow &17x
& = &-7\\\Leftrightarrow & \color{red}{17}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+7}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-x }
& = & 6 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 6 \color{blue}{-7} \\\Leftrightarrow &-9x
& = &-1\\\Leftrightarrow & \color{red}{-9}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)