Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(14x+8=14+x\)
- \(-7x+2=13+8x\)
- \(11x-5=-2+x\)
- \(-12x+11=-15+5x\)
- \(-15x+6=6+8x\)
- \(-5x-13=13+13x\)
- \(15x-14=4-14x\)
- \(-10x-1=-8+x\)
- \(7x-11=-2-10x\)
- \(9x+9=6-4x\)
- \(14x+2=-11+x\)
- \(-13x-7=7+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 14x \color{red}{+8}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8-x }
& = & 14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & 14 \color{blue}{-8} \\\Leftrightarrow &13x
& = &6\\\Leftrightarrow & \color{red}{13}x
& = &6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+2}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2-8x }
& = & 13 \color{red}{ +8x }\color{blue}{-2-8x } \\\Leftrightarrow & -7x \color{blue}{-8x }
& = & 13 \color{blue}{-2} \\\Leftrightarrow &-15x
& = &11\\\Leftrightarrow & \color{red}{-15}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-5}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5-x }
& = & -2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 11x \color{blue}{-x }
& = & -2 \color{blue}{+5} \\\Leftrightarrow &10x
& = &3\\\Leftrightarrow & \color{red}{10}x
& = &3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+11}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11-5x }
& = & -15 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & -12x \color{blue}{-5x }
& = & -15 \color{blue}{-11} \\\Leftrightarrow &-17x
& = &-26\\\Leftrightarrow & \color{red}{-17}x
& = &-26\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-26}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{26}{17} } & & \\ & V = \left\{ \frac{26}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+6}& = & 6 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-8x }
& = & 6 \color{red}{ +8x }\color{blue}{-6-8x } \\\Leftrightarrow & -15x \color{blue}{-8x }
& = & 6 \color{blue}{-6} \\\Leftrightarrow &-23x
& = &0\\\Leftrightarrow & \color{red}{-23}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{0}{-23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-13}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{-13}\color{blue}{+13-13x }
& = & 13 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -5x \color{blue}{-13x }
& = & 13 \color{blue}{+13} \\\Leftrightarrow &-18x
& = &26\\\Leftrightarrow & \color{red}{-18}x
& = &26\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}}
& = & \frac{26}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-14}& = & 4 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14+14x }
& = & 4 \color{red}{ -14x }\color{blue}{+14+14x } \\\Leftrightarrow & 15x \color{blue}{+14x }
& = & 4 \color{blue}{+14} \\\Leftrightarrow &29x
& = &18\\\Leftrightarrow & \color{red}{29}x
& = &18\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}}
& = & \frac{18}{29} \\\Leftrightarrow & \color{green}{ x = \frac{18}{29} } & & \\ & V = \left\{ \frac{18}{29} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-1}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-x }
& = & -8 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -8 \color{blue}{+1} \\\Leftrightarrow &-11x
& = &-7\\\Leftrightarrow & \color{red}{-11}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-11}& = & -2 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11+10x }
& = & -2 \color{red}{ -10x }\color{blue}{+11+10x } \\\Leftrightarrow & 7x \color{blue}{+10x }
& = & -2 \color{blue}{+11} \\\Leftrightarrow &17x
& = &9\\\Leftrightarrow & \color{red}{17}x
& = &9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+9}& = & 6 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9+4x }
& = & 6 \color{red}{ -4x }\color{blue}{-9+4x } \\\Leftrightarrow & 9x \color{blue}{+4x }
& = & 6 \color{blue}{-9} \\\Leftrightarrow &13x
& = &-3\\\Leftrightarrow & \color{red}{13}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-x }
& = & -11 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & -11 \color{blue}{-2} \\\Leftrightarrow &13x
& = &-13\\\Leftrightarrow & \color{red}{13}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-7}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-x }
& = & 7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 7 \color{blue}{+7} \\\Leftrightarrow &-14x
& = &14\\\Leftrightarrow & \color{red}{-14}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{14}{-14} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)