Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(5x+10=5-4x\)
- \(10x+15=13-3x\)
- \(12x+7=-2-11x\)
- \(6x+2=-12+5x\)
- \(7x+1=-15-3x\)
- \(-5x+7=11+8x\)
- \(-9x+7=14+x\)
- \(5x-4=-13-9x\)
- \(9x+5=10-11x\)
- \(9x-9=12+10x\)
- \(-2x-5=-14+x\)
- \(-5x+11=-6+3x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 5x \color{red}{+10}& = & 5 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10+4x }
& = & 5 \color{red}{ -4x }\color{blue}{-10+4x } \\\Leftrightarrow & 5x \color{blue}{+4x }
& = & 5 \color{blue}{-10} \\\Leftrightarrow &9x
& = &-5\\\Leftrightarrow & \color{red}{9}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+15}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15+3x }
& = & 13 \color{red}{ -3x }\color{blue}{-15+3x } \\\Leftrightarrow & 10x \color{blue}{+3x }
& = & 13 \color{blue}{-15} \\\Leftrightarrow &13x
& = &-2\\\Leftrightarrow & \color{red}{13}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+7}& = & -2 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7+11x }
& = & -2 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & -2 \color{blue}{-7} \\\Leftrightarrow &23x
& = &-9\\\Leftrightarrow & \color{red}{23}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-9}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{23} } & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+2}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2-5x }
& = & -12 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & 6x \color{blue}{-5x }
& = & -12 \color{blue}{-2} \\\Leftrightarrow &x
& = &-14\\\Leftrightarrow & \color{red}{}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -14 \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+1}& = & -15 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1+3x }
& = & -15 \color{red}{ -3x }\color{blue}{-1+3x } \\\Leftrightarrow & 7x \color{blue}{+3x }
& = & -15 \color{blue}{-1} \\\Leftrightarrow &10x
& = &-16\\\Leftrightarrow & \color{red}{10}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{-16}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+7}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-8x }
& = & 11 \color{red}{ +8x }\color{blue}{-7-8x } \\\Leftrightarrow & -5x \color{blue}{-8x }
& = & 11 \color{blue}{-7} \\\Leftrightarrow &-13x
& = &4\\\Leftrightarrow & \color{red}{-13}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-x }
& = & 14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 14 \color{blue}{-7} \\\Leftrightarrow &-10x
& = &7\\\Leftrightarrow & \color{red}{-10}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-4}& = & -13 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4+9x }
& = & -13 \color{red}{ -9x }\color{blue}{+4+9x } \\\Leftrightarrow & 5x \color{blue}{+9x }
& = & -13 \color{blue}{+4} \\\Leftrightarrow &14x
& = &-9\\\Leftrightarrow & \color{red}{14}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{-9}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+5}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5+11x }
& = & 10 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 9x \color{blue}{+11x }
& = & 10 \color{blue}{-5} \\\Leftrightarrow &20x
& = &5\\\Leftrightarrow & \color{red}{20}x
& = &5\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{5}{20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-9}& = & 12 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9-10x }
& = & 12 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & 9x \color{blue}{-10x }
& = & 12 \color{blue}{+9} \\\Leftrightarrow &-x
& = &21\\\Leftrightarrow & \color{red}{-}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{21}{-1} \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-5}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5-x }
& = & -14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & -14 \color{blue}{+5} \\\Leftrightarrow &-3x
& = &-9\\\Leftrightarrow & \color{red}{-3}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+11}& = & -6 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-3x }
& = & -6 \color{red}{ +3x }\color{blue}{-11-3x } \\\Leftrightarrow & -5x \color{blue}{-3x }
& = & -6 \color{blue}{-11} \\\Leftrightarrow &-8x
& = &-17\\\Leftrightarrow & \color{red}{-8}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{17}{8} } & & \\ & V = \left\{ \frac{17}{8} \right\} & \\\end{align}\)