Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(10x-14=-3+7x\)
- \(6x-15=-3-11x\)
- \(-15x-6=6+x\)
- \(-x+13=5+3x\)
- \(-5x-5=11+3x\)
- \(-12x-15=-10+13x\)
- \(6x+14=9-11x\)
- \(-7x-7=11+8x\)
- \(-13x+14=-1+14x\)
- \(-12x-11=-8+x\)
- \(-x-1=8+9x\)
- \(7x+4=12+11x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 10x \color{red}{-14}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14-7x }
& = & -3 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 10x \color{blue}{-7x }
& = & -3 \color{blue}{+14} \\\Leftrightarrow &3x
& = &11\\\Leftrightarrow & \color{red}{3}x
& = &11\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{11}{3} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-15}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15+11x }
& = & -3 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & -3 \color{blue}{+15} \\\Leftrightarrow &17x
& = &12\\\Leftrightarrow & \color{red}{17}x
& = &12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-x }
& = & 6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & 6 \color{blue}{+6} \\\Leftrightarrow &-16x
& = &12\\\Leftrightarrow & \color{red}{-16}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+13}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13-3x }
& = & 5 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & -x \color{blue}{-3x }
& = & 5 \color{blue}{-13} \\\Leftrightarrow &-4x
& = &-8\\\Leftrightarrow & \color{red}{-4}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-8}{-4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-5}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-3x }
& = & 11 \color{red}{ +3x }\color{blue}{+5-3x } \\\Leftrightarrow & -5x \color{blue}{-3x }
& = & 11 \color{blue}{+5} \\\Leftrightarrow &-8x
& = &16\\\Leftrightarrow & \color{red}{-8}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{16}{-8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-15}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15-13x }
& = & -10 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & -10 \color{blue}{+15} \\\Leftrightarrow &-25x
& = &5\\\Leftrightarrow & \color{red}{-25}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{5}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+14}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14+11x }
& = & 9 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & 9 \color{blue}{-14} \\\Leftrightarrow &17x
& = &-5\\\Leftrightarrow & \color{red}{17}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{17} } & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-7}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-8x }
& = & 11 \color{red}{ +8x }\color{blue}{+7-8x } \\\Leftrightarrow & -7x \color{blue}{-8x }
& = & 11 \color{blue}{+7} \\\Leftrightarrow &-15x
& = &18\\\Leftrightarrow & \color{red}{-15}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+14}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-14x }
& = & -1 \color{red}{ +14x }\color{blue}{-14-14x } \\\Leftrightarrow & -13x \color{blue}{-14x }
& = & -1 \color{blue}{-14} \\\Leftrightarrow &-27x
& = &-15\\\Leftrightarrow & \color{red}{-27}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}}
& = & \frac{-15}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-11}\color{blue}{+11-x }
& = & -8 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -8 \color{blue}{+11} \\\Leftrightarrow &-13x
& = &3\\\Leftrightarrow & \color{red}{-13}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-1}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1-9x }
& = & 8 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & -x \color{blue}{-9x }
& = & 8 \color{blue}{+1} \\\Leftrightarrow &-10x
& = &9\\\Leftrightarrow & \color{red}{-10}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+4}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4-11x }
& = & 12 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 7x \color{blue}{-11x }
& = & 12 \color{blue}{-4} \\\Leftrightarrow &-4x
& = &8\\\Leftrightarrow & \color{red}{-4}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)