Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-12x+1=-12+x\)
- \(7x+10=-13-6x\)
- \(7x-1=-6+9x\)
- \(3x-12=11+8x\)
- \(-12x+14=7+x\)
- \(5x-4=1-9x\)
- \(14x-11=-15+x\)
- \(-6x+8=-1+x\)
- \(14x+2=8+5x\)
- \(5x-10=11-14x\)
- \(8x+15=-12+9x\)
- \(-12x-6=5+13x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -12x \color{red}{+1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-x }
& = & -12 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -12 \color{blue}{-1} \\\Leftrightarrow &-13x
& = &-13\\\Leftrightarrow & \color{red}{-13}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+10}& = & -13 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10+6x }
& = & -13 \color{red}{ -6x }\color{blue}{-10+6x } \\\Leftrightarrow & 7x \color{blue}{+6x }
& = & -13 \color{blue}{-10} \\\Leftrightarrow &13x
& = &-23\\\Leftrightarrow & \color{red}{13}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-23}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{13} } & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-1}& = & -6 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1-9x }
& = & -6 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & 7x \color{blue}{-9x }
& = & -6 \color{blue}{+1} \\\Leftrightarrow &-2x
& = &-5\\\Leftrightarrow & \color{red}{-2}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}}
& = & \frac{-5}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-12}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12-8x }
& = & 11 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & 3x \color{blue}{-8x }
& = & 11 \color{blue}{+12} \\\Leftrightarrow &-5x
& = &23\\\Leftrightarrow & \color{red}{-5}x
& = &23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{5} } & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-x }
& = & 7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 7 \color{blue}{-14} \\\Leftrightarrow &-13x
& = &-7\\\Leftrightarrow & \color{red}{-13}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-4}& = & 1 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4+9x }
& = & 1 \color{red}{ -9x }\color{blue}{+4+9x } \\\Leftrightarrow & 5x \color{blue}{+9x }
& = & 1 \color{blue}{+4} \\\Leftrightarrow &14x
& = &5\\\Leftrightarrow & \color{red}{14}x
& = &5\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{5}{14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-11}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11-x }
& = & -15 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & -15 \color{blue}{+11} \\\Leftrightarrow &13x
& = &-4\\\Leftrightarrow & \color{red}{13}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+8}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-x }
& = & -1 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -1 \color{blue}{-8} \\\Leftrightarrow &-7x
& = &-9\\\Leftrightarrow & \color{red}{-7}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+2}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-5x }
& = & 8 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & 14x \color{blue}{-5x }
& = & 8 \color{blue}{-2} \\\Leftrightarrow &9x
& = &6\\\Leftrightarrow & \color{red}{9}x
& = &6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-10}& = & 11 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10+14x }
& = & 11 \color{red}{ -14x }\color{blue}{+10+14x } \\\Leftrightarrow & 5x \color{blue}{+14x }
& = & 11 \color{blue}{+10} \\\Leftrightarrow &19x
& = &21\\\Leftrightarrow & \color{red}{19}x
& = &21\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{21}{19} \\\Leftrightarrow & \color{green}{ x = \frac{21}{19} } & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+15}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-9x }
& = & -12 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & 8x \color{blue}{-9x }
& = & -12 \color{blue}{-15} \\\Leftrightarrow &-x
& = &-27\\\Leftrightarrow & \color{red}{-}x
& = &-27\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-27}{-1} \\\Leftrightarrow & \color{green}{ x = 27 } & & \\ & V = \left\{ 27 \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-6}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-13x }
& = & 5 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & 5 \color{blue}{+6} \\\Leftrightarrow &-25x
& = &11\\\Leftrightarrow & \color{red}{-25}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{11}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{25} } & & \\ & V = \left\{ \frac{-11}{25} \right\} & \\\end{align}\)