Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(7x+8=-4-3x\)
- \(13x-1=13+9x\)
- \(-15x+3=1+13x\)
- \(-13x-4=-5+x\)
- \(10x-6=-3-3x\)
- \(-11x-11=-6+x\)
- \(6x-1=15-11x\)
- \(8x+7=-5+3x\)
- \(9x-2=6-11x\)
- \(-8x+8=5+9x\)
- \(15x+9=-13+x\)
- \(7x+9=-4+12x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 7x \color{red}{+8}& = & -4 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8+3x }
& = & -4 \color{red}{ -3x }\color{blue}{-8+3x } \\\Leftrightarrow & 7x \color{blue}{+3x }
& = & -4 \color{blue}{-8} \\\Leftrightarrow &10x
& = &-12\\\Leftrightarrow & \color{red}{10}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{-12}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-1}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1-9x }
& = & 13 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & 13x \color{blue}{-9x }
& = & 13 \color{blue}{+1} \\\Leftrightarrow &4x
& = &14\\\Leftrightarrow & \color{red}{4}x
& = &14\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{14}{4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+3}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+3}\color{blue}{-3-13x }
& = & 1 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & 1 \color{blue}{-3} \\\Leftrightarrow &-28x
& = &-2\\\Leftrightarrow & \color{red}{-28}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{-2}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-4}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-4}\color{blue}{+4-x }
& = & -5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -5 \color{blue}{+4} \\\Leftrightarrow &-14x
& = &-1\\\Leftrightarrow & \color{red}{-14}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-6}& = & -3 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6+3x }
& = & -3 \color{red}{ -3x }\color{blue}{+6+3x } \\\Leftrightarrow & 10x \color{blue}{+3x }
& = & -3 \color{blue}{+6} \\\Leftrightarrow &13x
& = &3\\\Leftrightarrow & \color{red}{13}x
& = &3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-11}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-x }
& = & -6 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -6 \color{blue}{+11} \\\Leftrightarrow &-12x
& = &5\\\Leftrightarrow & \color{red}{-12}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-1}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1+11x }
& = & 15 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & 15 \color{blue}{+1} \\\Leftrightarrow &17x
& = &16\\\Leftrightarrow & \color{red}{17}x
& = &16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+7}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7-3x }
& = & -5 \color{red}{ +3x }\color{blue}{-7-3x } \\\Leftrightarrow & 8x \color{blue}{-3x }
& = & -5 \color{blue}{-7} \\\Leftrightarrow &5x
& = &-12\\\Leftrightarrow & \color{red}{5}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-2}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2+11x }
& = & 6 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 9x \color{blue}{+11x }
& = & 6 \color{blue}{+2} \\\Leftrightarrow &20x
& = &8\\\Leftrightarrow & \color{red}{20}x
& = &8\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{8}{20} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+8}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-9x }
& = & 5 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & -8x \color{blue}{-9x }
& = & 5 \color{blue}{-8} \\\Leftrightarrow &-17x
& = &-3\\\Leftrightarrow & \color{red}{-17}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9-x }
& = & -13 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 15x \color{blue}{-x }
& = & -13 \color{blue}{-9} \\\Leftrightarrow &14x
& = &-22\\\Leftrightarrow & \color{red}{14}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{-22}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+9}& = & -4 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9-12x }
& = & -4 \color{red}{ +12x }\color{blue}{-9-12x } \\\Leftrightarrow & 7x \color{blue}{-12x }
& = & -4 \color{blue}{-9} \\\Leftrightarrow &-5x
& = &-13\\\Leftrightarrow & \color{red}{-5}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)