Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-x-10=14+15x\)
- \(7x+6=14-3x\)
- \(-15x-6=-6+x\)
- \(-15x+6=14+x\)
- \(5x-2=11-9x\)
- \(9x-12=4+11x\)
- \(2x+12=-15+x\)
- \(13x-2=5+14x\)
- \(-12x-3=7+x\)
- \(7x-12=11+8x\)
- \(-11x+15=-12+x\)
- \(-11x-2=-10+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -x \color{red}{-10}& = & 14 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10-15x }
& = & 14 \color{red}{ +15x }\color{blue}{+10-15x } \\\Leftrightarrow & -x \color{blue}{-15x }
& = & 14 \color{blue}{+10} \\\Leftrightarrow &-16x
& = &24\\\Leftrightarrow & \color{red}{-16}x
& = &24\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{24}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+6}& = & 14 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6+3x }
& = & 14 \color{red}{ -3x }\color{blue}{-6+3x } \\\Leftrightarrow & 7x \color{blue}{+3x }
& = & 14 \color{blue}{-6} \\\Leftrightarrow &10x
& = &8\\\Leftrightarrow & \color{red}{10}x
& = &8\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{8}{10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-6}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-x }
& = & -6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & -6 \color{blue}{+6} \\\Leftrightarrow &-16x
& = &0\\\Leftrightarrow & \color{red}{-16}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+6}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-x }
& = & 14 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & 14 \color{blue}{-6} \\\Leftrightarrow &-16x
& = &8\\\Leftrightarrow & \color{red}{-16}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-2}& = & 11 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2+9x }
& = & 11 \color{red}{ -9x }\color{blue}{+2+9x } \\\Leftrightarrow & 5x \color{blue}{+9x }
& = & 11 \color{blue}{+2} \\\Leftrightarrow &14x
& = &13\\\Leftrightarrow & \color{red}{14}x
& = &13\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{13}{14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-12}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12-11x }
& = & 4 \color{red}{ +11x }\color{blue}{+12-11x } \\\Leftrightarrow & 9x \color{blue}{-11x }
& = & 4 \color{blue}{+12} \\\Leftrightarrow &-2x
& = &16\\\Leftrightarrow & \color{red}{-2}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}}
& = & \frac{16}{-2} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+12}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-x }
& = & -15 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & -15 \color{blue}{-12} \\\Leftrightarrow &x
& = &-27\\\Leftrightarrow & \color{red}{}x
& = &-27\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -27 \\\Leftrightarrow & \color{green}{ x = -27 } & & \\ & V = \left\{ -27 \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-2}& = & 5 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2-14x }
& = & 5 \color{red}{ +14x }\color{blue}{+2-14x } \\\Leftrightarrow & 13x \color{blue}{-14x }
& = & 5 \color{blue}{+2} \\\Leftrightarrow &-x
& = &7\\\Leftrightarrow & \color{red}{-}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-x }
& = & 7 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 7 \color{blue}{+3} \\\Leftrightarrow &-13x
& = &10\\\Leftrightarrow & \color{red}{-13}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-12}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-8x }
& = & 11 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & 7x \color{blue}{-8x }
& = & 11 \color{blue}{+12} \\\Leftrightarrow &-x
& = &23\\\Leftrightarrow & \color{red}{-}x
& = &23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{23}{-1} \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+15}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-x }
& = & -12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -12 \color{blue}{-15} \\\Leftrightarrow &-12x
& = &-27\\\Leftrightarrow & \color{red}{-12}x
& = &-27\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-27}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-x }
& = & -10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -10 \color{blue}{+2} \\\Leftrightarrow &-12x
& = &-8\\\Leftrightarrow & \color{red}{-12}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)