Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-4x+5=-2+x\)
- \(-3x-9=13+x\)
- \(-4x-12=-7+x\)
- \(-14x-8=5+x\)
- \(x+14=3+10x\)
- \(6x-4=8+7x\)
- \(5x-4=5+x\)
- \(12x+9=-14-11x\)
- \(-6x+1=-10+x\)
- \(-6x-5=-8+7x\)
- \(-9x+4=-6+x\)
- \(-x+7=-14+5x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -4x \color{red}{+5}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5-x }
& = & -2 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -2 \color{blue}{-5} \\\Leftrightarrow &-5x
& = &-7\\\Leftrightarrow & \color{red}{-5}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-x }
& = & 13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 13 \color{blue}{+9} \\\Leftrightarrow &-4x
& = &22\\\Leftrightarrow & \color{red}{-4}x
& = &22\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{22}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-12}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-12}\color{blue}{+12-x }
& = & -7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -7 \color{blue}{+12} \\\Leftrightarrow &-5x
& = &5\\\Leftrightarrow & \color{red}{-5}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-8}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x }
& = & 5 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 5 \color{blue}{+8} \\\Leftrightarrow &-15x
& = &13\\\Leftrightarrow & \color{red}{-15}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+14}& = & 3 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14-10x }
& = & 3 \color{red}{ +10x }\color{blue}{-14-10x } \\\Leftrightarrow & x \color{blue}{-10x }
& = & 3 \color{blue}{-14} \\\Leftrightarrow &-9x
& = &-11\\\Leftrightarrow & \color{red}{-9}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-4}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4-7x }
& = & 8 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & 6x \color{blue}{-7x }
& = & 8 \color{blue}{+4} \\\Leftrightarrow &-x
& = &12\\\Leftrightarrow & \color{red}{-}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{12}{-1} \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4-x }
& = & 5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 5x \color{blue}{-x }
& = & 5 \color{blue}{+4} \\\Leftrightarrow &4x
& = &9\\\Leftrightarrow & \color{red}{4}x
& = &9\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{9}{4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+9}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9+11x }
& = & -14 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & -14 \color{blue}{-9} \\\Leftrightarrow &23x
& = &-23\\\Leftrightarrow & \color{red}{23}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-23}{23} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-x }
& = & -10 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -10 \color{blue}{-1} \\\Leftrightarrow &-7x
& = &-11\\\Leftrightarrow & \color{red}{-7}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-5}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-7x }
& = & -8 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & -8 \color{blue}{+5} \\\Leftrightarrow &-13x
& = &-3\\\Leftrightarrow & \color{red}{-13}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-x }
& = & -6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -6 \color{blue}{-4} \\\Leftrightarrow &-10x
& = &-10\\\Leftrightarrow & \color{red}{-10}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-10}{-10} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+7}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7-5x }
& = & -14 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -x \color{blue}{-5x }
& = & -14 \color{blue}{-7} \\\Leftrightarrow &-6x
& = &-21\\\Leftrightarrow & \color{red}{-6}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-21}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)