Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(11x+14=5-8x\)
- \(-15x-2=-2+x\)
- \(13x+3=-7-12x\)
- \(3x-6=9+x\)
- \(6x-1=13-11x\)
- \(3x+9=7-8x\)
- \(-9x-13=1+10x\)
- \(5x+14=6+11x\)
- \(5x+7=1-9x\)
- \(-10x+5=-10+7x\)
- \(-6x+1=4+7x\)
- \(6x-2=15+11x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 11x \color{red}{+14}& = & 5 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14+8x }
& = & 5 \color{red}{ -8x }\color{blue}{-14+8x } \\\Leftrightarrow & 11x \color{blue}{+8x }
& = & 5 \color{blue}{-14} \\\Leftrightarrow &19x
& = &-9\\\Leftrightarrow & \color{red}{19}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-2}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-x }
& = & -2 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & -2 \color{blue}{+2} \\\Leftrightarrow &-16x
& = &0\\\Leftrightarrow & \color{red}{-16}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+3}& = & -7 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3+12x }
& = & -7 \color{red}{ -12x }\color{blue}{-3+12x } \\\Leftrightarrow & 13x \color{blue}{+12x }
& = & -7 \color{blue}{-3} \\\Leftrightarrow &25x
& = &-10\\\Leftrightarrow & \color{red}{25}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{-10}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-6}\color{blue}{+6-x }
& = & 9 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 3x \color{blue}{-x }
& = & 9 \color{blue}{+6} \\\Leftrightarrow &2x
& = &15\\\Leftrightarrow & \color{red}{2}x
& = &15\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{15}{2} \\\Leftrightarrow & \color{green}{ x = \frac{15}{2} } & & \\ & V = \left\{ \frac{15}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-1}& = & 13 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1+11x }
& = & 13 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & 13 \color{blue}{+1} \\\Leftrightarrow &17x
& = &14\\\Leftrightarrow & \color{red}{17}x
& = &14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+9}& = & 7 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9+8x }
& = & 7 \color{red}{ -8x }\color{blue}{-9+8x } \\\Leftrightarrow & 3x \color{blue}{+8x }
& = & 7 \color{blue}{-9} \\\Leftrightarrow &11x
& = &-2\\\Leftrightarrow & \color{red}{11}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-13}& = & 1 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13-10x }
& = & 1 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & -9x \color{blue}{-10x }
& = & 1 \color{blue}{+13} \\\Leftrightarrow &-19x
& = &14\\\Leftrightarrow & \color{red}{-19}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{14}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{19} } & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+14}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14-11x }
& = & 6 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & 5x \color{blue}{-11x }
& = & 6 \color{blue}{-14} \\\Leftrightarrow &-6x
& = &-8\\\Leftrightarrow & \color{red}{-6}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+7}& = & 1 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7+9x }
& = & 1 \color{red}{ -9x }\color{blue}{-7+9x } \\\Leftrightarrow & 5x \color{blue}{+9x }
& = & 1 \color{blue}{-7} \\\Leftrightarrow &14x
& = &-6\\\Leftrightarrow & \color{red}{14}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{-6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+5}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-7x }
& = & -10 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -10x \color{blue}{-7x }
& = & -10 \color{blue}{-5} \\\Leftrightarrow &-17x
& = &-15\\\Leftrightarrow & \color{red}{-17}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-15}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{15}{17} } & & \\ & V = \left\{ \frac{15}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+1}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-7x }
& = & 4 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & 4 \color{blue}{-1} \\\Leftrightarrow &-13x
& = &3\\\Leftrightarrow & \color{red}{-13}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-2}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2-11x }
& = & 15 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & 6x \color{blue}{-11x }
& = & 15 \color{blue}{+2} \\\Leftrightarrow &-5x
& = &17\\\Leftrightarrow & \color{red}{-5}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{17}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{5} } & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)