Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(5x+8=2+13x\)
- \(10x+12=11-13x\)
- \(-9x-4=-4+5x\)
- \(x-13=-8-5x\)
- \(3x+2=-13-11x\)
- \(14x+10=4-11x\)
- \(-9x+1=-11+x\)
- \(-6x+14=-1+13x\)
- \(-6x+3=1+7x\)
- \(-13x-15=-13+7x\)
- \(-9x+2=-9+5x\)
- \(12x-15=12+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 5x \color{red}{+8}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8-13x }
& = & 2 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & 5x \color{blue}{-13x }
& = & 2 \color{blue}{-8} \\\Leftrightarrow &-8x
& = &-6\\\Leftrightarrow & \color{red}{-8}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+12}& = & 11 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12+13x }
& = & 11 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 10x \color{blue}{+13x }
& = & 11 \color{blue}{-12} \\\Leftrightarrow &23x
& = &-1\\\Leftrightarrow & \color{red}{23}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-4}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-4}\color{blue}{+4-5x }
& = & -4 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & -9x \color{blue}{-5x }
& = & -4 \color{blue}{+4} \\\Leftrightarrow &-14x
& = &0\\\Leftrightarrow & \color{red}{-14}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-13}& = & -8 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13+5x }
& = & -8 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & x \color{blue}{+5x }
& = & -8 \color{blue}{+13} \\\Leftrightarrow &6x
& = &5\\\Leftrightarrow & \color{red}{6}x
& = &5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}}
& = & \frac{5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+2}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2+11x }
& = & -13 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 3x \color{blue}{+11x }
& = & -13 \color{blue}{-2} \\\Leftrightarrow &14x
& = &-15\\\Leftrightarrow & \color{red}{14}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{-15}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{14} } & & \\ & V = \left\{ \frac{-15}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+10}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10+11x }
& = & 4 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 14x \color{blue}{+11x }
& = & 4 \color{blue}{-10} \\\Leftrightarrow &25x
& = &-6\\\Leftrightarrow & \color{red}{25}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{-6}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{25} } & & \\ & V = \left\{ \frac{-6}{25} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+1}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-x }
& = & -11 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -11 \color{blue}{-1} \\\Leftrightarrow &-10x
& = &-12\\\Leftrightarrow & \color{red}{-10}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-12}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+14}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-13x }
& = & -1 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & -1 \color{blue}{-14} \\\Leftrightarrow &-19x
& = &-15\\\Leftrightarrow & \color{red}{-19}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-15}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{15}{19} } & & \\ & V = \left\{ \frac{15}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+3}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-7x }
& = & 1 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & 1 \color{blue}{-3} \\\Leftrightarrow &-13x
& = &-2\\\Leftrightarrow & \color{red}{-13}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-15}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-7x }
& = & -13 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -13x \color{blue}{-7x }
& = & -13 \color{blue}{+15} \\\Leftrightarrow &-20x
& = &2\\\Leftrightarrow & \color{red}{-20}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{2}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+2}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-5x }
& = & -9 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & -9x \color{blue}{-5x }
& = & -9 \color{blue}{-2} \\\Leftrightarrow &-14x
& = &-11\\\Leftrightarrow & \color{red}{-14}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{11}{14} } & & \\ & V = \left\{ \frac{11}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15-x }
& = & 12 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & 12 \color{blue}{+15} \\\Leftrightarrow &11x
& = &27\\\Leftrightarrow & \color{red}{11}x
& = &27\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{27}{11} \\\Leftrightarrow & \color{green}{ x = \frac{27}{11} } & & \\ & V = \left\{ \frac{27}{11} \right\} & \\\end{align}\)