Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-x+5=12+x\)
- \(-2x+15=-15+3x\)
- \(-15x-5=-2+13x\)
- \(7x-4=9+3x\)
- \(-2x-14=4+x\)
- \(-4x+1=-8+5x\)
- \(-5x-9=-8+11x\)
- \(-3x+8=-1+x\)
- \(9x-11=-10+10x\)
- \(7x+10=9-13x\)
- \(13x-6=10+7x\)
- \(-6x+12=-9+13x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -x \color{red}{+5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5-x }
& = & 12 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -x \color{blue}{-x }
& = & 12 \color{blue}{-5} \\\Leftrightarrow &-2x
& = &7\\\Leftrightarrow & \color{red}{-2}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}}
& = & \frac{7}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+15}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15-3x }
& = & -15 \color{red}{ +3x }\color{blue}{-15-3x } \\\Leftrightarrow & -2x \color{blue}{-3x }
& = & -15 \color{blue}{-15} \\\Leftrightarrow &-5x
& = &-30\\\Leftrightarrow & \color{red}{-5}x
& = &-30\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-30}{-5} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-5}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5-13x }
& = & -2 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & -2 \color{blue}{+5} \\\Leftrightarrow &-28x
& = &3\\\Leftrightarrow & \color{red}{-28}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{3}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{28} } & & \\ & V = \left\{ \frac{-3}{28} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-4}& = & 9 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4-3x }
& = & 9 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & 7x \color{blue}{-3x }
& = & 9 \color{blue}{+4} \\\Leftrightarrow &4x
& = &13\\\Leftrightarrow & \color{red}{4}x
& = &13\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{13}{4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14-x }
& = & 4 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & 4 \color{blue}{+14} \\\Leftrightarrow &-3x
& = &18\\\Leftrightarrow & \color{red}{-3}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{18}{-3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+1}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-5x }
& = & -8 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -4x \color{blue}{-5x }
& = & -8 \color{blue}{-1} \\\Leftrightarrow &-9x
& = &-9\\\Leftrightarrow & \color{red}{-9}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-9}{-9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-9}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-11x }
& = & -8 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & -5x \color{blue}{-11x }
& = & -8 \color{blue}{+9} \\\Leftrightarrow &-16x
& = &1\\\Leftrightarrow & \color{red}{-16}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+8}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-x }
& = & -1 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -1 \color{blue}{-8} \\\Leftrightarrow &-4x
& = &-9\\\Leftrightarrow & \color{red}{-4}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-11}& = & -10 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11-10x }
& = & -10 \color{red}{ +10x }\color{blue}{+11-10x } \\\Leftrightarrow & 9x \color{blue}{-10x }
& = & -10 \color{blue}{+11} \\\Leftrightarrow &-x
& = &1\\\Leftrightarrow & \color{red}{-}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{1}{-1} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+10}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10+13x }
& = & 9 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 7x \color{blue}{+13x }
& = & 9 \color{blue}{-10} \\\Leftrightarrow &20x
& = &-1\\\Leftrightarrow & \color{red}{20}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{-1}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{20} } & & \\ & V = \left\{ \frac{-1}{20} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-6}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6-7x }
& = & 10 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 13x \color{blue}{-7x }
& = & 10 \color{blue}{+6} \\\Leftrightarrow &6x
& = &16\\\Leftrightarrow & \color{red}{6}x
& = &16\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}}
& = & \frac{16}{6} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+12}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12-13x }
& = & -9 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & -9 \color{blue}{-12} \\\Leftrightarrow &-19x
& = &-21\\\Leftrightarrow & \color{red}{-19}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-21}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{21}{19} } & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)