Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(15x-9=-6-7x\)
- \(-6x+5=-11+x\)
- \(-8x-7=-7+9x\)
- \(-10x-4=-1+7x\)
- \(-12x-7=7+5x\)
- \(5x-15=12+8x\)
- \(-4x-4=3+x\)
- \(8x-12=-9+13x\)
- \(-4x+9=-15+5x\)
- \(13x-13=4+4x\)
- \(14x-8=11+11x\)
- \(-14x-10=-11+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 15x \color{red}{-9}& = & -6 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9+7x }
& = & -6 \color{red}{ -7x }\color{blue}{+9+7x } \\\Leftrightarrow & 15x \color{blue}{+7x }
& = & -6 \color{blue}{+9} \\\Leftrightarrow &22x
& = &3\\\Leftrightarrow & \color{red}{22}x
& = &3\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}}
& = & \frac{3}{22} \\\Leftrightarrow & \color{green}{ x = \frac{3}{22} } & & \\ & V = \left\{ \frac{3}{22} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+5}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-x }
& = & -11 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -11 \color{blue}{-5} \\\Leftrightarrow &-7x
& = &-16\\\Leftrightarrow & \color{red}{-7}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-7}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-7}\color{blue}{+7-9x }
& = & -7 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -8x \color{blue}{-9x }
& = & -7 \color{blue}{+7} \\\Leftrightarrow &-17x
& = &0\\\Leftrightarrow & \color{red}{-17}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{0}{-17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-4}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-7x }
& = & -1 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & -10x \color{blue}{-7x }
& = & -1 \color{blue}{+4} \\\Leftrightarrow &-17x
& = &3\\\Leftrightarrow & \color{red}{-17}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-7}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-5x }
& = & 7 \color{red}{ +5x }\color{blue}{+7-5x } \\\Leftrightarrow & -12x \color{blue}{-5x }
& = & 7 \color{blue}{+7} \\\Leftrightarrow &-17x
& = &14\\\Leftrightarrow & \color{red}{-17}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-15}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{-15}\color{blue}{+15-8x }
& = & 12 \color{red}{ +8x }\color{blue}{+15-8x } \\\Leftrightarrow & 5x \color{blue}{-8x }
& = & 12 \color{blue}{+15} \\\Leftrightarrow &-3x
& = &27\\\Leftrightarrow & \color{red}{-3}x
& = &27\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{27}{-3} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-4}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-x }
& = & 3 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & 3 \color{blue}{+4} \\\Leftrightarrow &-5x
& = &7\\\Leftrightarrow & \color{red}{-5}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-12}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12-13x }
& = & -9 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 8x \color{blue}{-13x }
& = & -9 \color{blue}{+12} \\\Leftrightarrow &-5x
& = &3\\\Leftrightarrow & \color{red}{-5}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+9}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-5x }
& = & -15 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & -4x \color{blue}{-5x }
& = & -15 \color{blue}{-9} \\\Leftrightarrow &-9x
& = &-24\\\Leftrightarrow & \color{red}{-9}x
& = &-24\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-24}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-13}& = & 4 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13-4x }
& = & 4 \color{red}{ +4x }\color{blue}{+13-4x } \\\Leftrightarrow & 13x \color{blue}{-4x }
& = & 4 \color{blue}{+13} \\\Leftrightarrow &9x
& = &17\\\Leftrightarrow & \color{red}{9}x
& = &17\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{17}{9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-8}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-11x }
& = & 11 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & 14x \color{blue}{-11x }
& = & 11 \color{blue}{+8} \\\Leftrightarrow &3x
& = &19\\\Leftrightarrow & \color{red}{3}x
& = &19\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{19}{3} \\\Leftrightarrow & \color{green}{ x = \frac{19}{3} } & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-10}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10-x }
& = & -11 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -11 \color{blue}{+10} \\\Leftrightarrow &-15x
& = &-1\\\Leftrightarrow & \color{red}{-15}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)