Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(8x-11=-15-5x\)
- \(10x+7=3-3x\)
- \(9x+15=13+5x\)
- \(-9x+6=15+10x\)
- \(-7x-6=-12+11x\)
- \(11x-3=-6+14x\)
- \(-15x-12=12+x\)
- \(-11x-14=-3+x\)
- \(-x-1=2-2x\)
- \(6x-14=4+11x\)
- \(-3x+11=10+x\)
- \(3x+11=6-8x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 8x \color{red}{-11}& = & -15 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11+5x }
& = & -15 \color{red}{ -5x }\color{blue}{+11+5x } \\\Leftrightarrow & 8x \color{blue}{+5x }
& = & -15 \color{blue}{+11} \\\Leftrightarrow &13x
& = &-4\\\Leftrightarrow & \color{red}{13}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+7}& = & 3 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7+3x }
& = & 3 \color{red}{ -3x }\color{blue}{-7+3x } \\\Leftrightarrow & 10x \color{blue}{+3x }
& = & 3 \color{blue}{-7} \\\Leftrightarrow &13x
& = &-4\\\Leftrightarrow & \color{red}{13}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+15}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15-5x }
& = & 13 \color{red}{ +5x }\color{blue}{-15-5x } \\\Leftrightarrow & 9x \color{blue}{-5x }
& = & 13 \color{blue}{-15} \\\Leftrightarrow &4x
& = &-2\\\Leftrightarrow & \color{red}{4}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{-2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+6}& = & 15 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-10x }
& = & 15 \color{red}{ +10x }\color{blue}{-6-10x } \\\Leftrightarrow & -9x \color{blue}{-10x }
& = & 15 \color{blue}{-6} \\\Leftrightarrow &-19x
& = &9\\\Leftrightarrow & \color{red}{-19}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-6}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-11x }
& = & -12 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & -7x \color{blue}{-11x }
& = & -12 \color{blue}{+6} \\\Leftrightarrow &-18x
& = &-6\\\Leftrightarrow & \color{red}{-18}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}}
& = & \frac{-6}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-3}& = & -6 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3-14x }
& = & -6 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & 11x \color{blue}{-14x }
& = & -6 \color{blue}{+3} \\\Leftrightarrow &-3x
& = &-3\\\Leftrightarrow & \color{red}{-3}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-x }
& = & 12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & 12 \color{blue}{+12} \\\Leftrightarrow &-16x
& = &24\\\Leftrightarrow & \color{red}{-16}x
& = &24\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{24}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-14}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-x }
& = & -3 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -3 \color{blue}{+14} \\\Leftrightarrow &-12x
& = &11\\\Leftrightarrow & \color{red}{-12}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{11}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-1}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1+2x }
& = & 2 \color{red}{ -2x }\color{blue}{+1+2x } \\\Leftrightarrow & -x \color{blue}{+2x }
& = & 2 \color{blue}{+1} \\\Leftrightarrow &x
& = &3\\\Leftrightarrow & \color{red}{}x
& = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-14}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14-11x }
& = & 4 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & 6x \color{blue}{-11x }
& = & 4 \color{blue}{+14} \\\Leftrightarrow &-5x
& = &18\\\Leftrightarrow & \color{red}{-5}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+11}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-x }
& = & 10 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 10 \color{blue}{-11} \\\Leftrightarrow &-4x
& = &-1\\\Leftrightarrow & \color{red}{-4}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+11}& = & 6 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11+8x }
& = & 6 \color{red}{ -8x }\color{blue}{-11+8x } \\\Leftrightarrow & 3x \color{blue}{+8x }
& = & 6 \color{blue}{-11} \\\Leftrightarrow &11x
& = &-5\\\Leftrightarrow & \color{red}{11}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)