Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(4x-15=-13-7x\)
- \(-12x+1=-7+x\)
- \(-12x-1=-13+x\)
- \(-2x-11=-3+x\)
- \(-x+15=-3-8x\)
- \(-4x-14=5+x\)
- \(-2x+2=-2+x\)
- \(9x+6=-14-2x\)
- \(9x-9=-12+2x\)
- \(13x-5=14-6x\)
- \(8x+7=-14-15x\)
- \(3x-11=-2-5x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 4x \color{red}{-15}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15+7x }
& = & -13 \color{red}{ -7x }\color{blue}{+15+7x } \\\Leftrightarrow & 4x \color{blue}{+7x }
& = & -13 \color{blue}{+15} \\\Leftrightarrow &11x
& = &2\\\Leftrightarrow & \color{red}{11}x
& = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+1}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-x }
& = & -7 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -7 \color{blue}{-1} \\\Leftrightarrow &-13x
& = &-8\\\Leftrightarrow & \color{red}{-13}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-1}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-x }
& = & -13 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -13 \color{blue}{+1} \\\Leftrightarrow &-13x
& = &-12\\\Leftrightarrow & \color{red}{-13}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-11}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11-x }
& = & -3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & -3 \color{blue}{+11} \\\Leftrightarrow &-3x
& = &8\\\Leftrightarrow & \color{red}{-3}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+15}& = & -3 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15+8x }
& = & -3 \color{red}{ -8x }\color{blue}{-15+8x } \\\Leftrightarrow & -x \color{blue}{+8x }
& = & -3 \color{blue}{-15} \\\Leftrightarrow &7x
& = &-18\\\Leftrightarrow & \color{red}{7}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{-18}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14-x }
& = & 5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & 5 \color{blue}{+14} \\\Leftrightarrow &-5x
& = &19\\\Leftrightarrow & \color{red}{-5}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+2}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2-x }
& = & -2 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & -2 \color{blue}{-2} \\\Leftrightarrow &-3x
& = &-4\\\Leftrightarrow & \color{red}{-3}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+6}& = & -14 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6+2x }
& = & -14 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 9x \color{blue}{+2x }
& = & -14 \color{blue}{-6} \\\Leftrightarrow &11x
& = &-20\\\Leftrightarrow & \color{red}{11}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-9}& = & -12 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9-2x }
& = & -12 \color{red}{ +2x }\color{blue}{+9-2x } \\\Leftrightarrow & 9x \color{blue}{-2x }
& = & -12 \color{blue}{+9} \\\Leftrightarrow &7x
& = &-3\\\Leftrightarrow & \color{red}{7}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-5}& = & 14 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5+6x }
& = & 14 \color{red}{ -6x }\color{blue}{+5+6x } \\\Leftrightarrow & 13x \color{blue}{+6x }
& = & 14 \color{blue}{+5} \\\Leftrightarrow &19x
& = &19\\\Leftrightarrow & \color{red}{19}x
& = &19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{19}{19} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+7}& = & -14 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7+15x }
& = & -14 \color{red}{ -15x }\color{blue}{-7+15x } \\\Leftrightarrow & 8x \color{blue}{+15x }
& = & -14 \color{blue}{-7} \\\Leftrightarrow &23x
& = &-21\\\Leftrightarrow & \color{red}{23}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-21}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{23} } & & \\ & V = \left\{ \frac{-21}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-11}& = & -2 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11+5x }
& = & -2 \color{red}{ -5x }\color{blue}{+11+5x } \\\Leftrightarrow & 3x \color{blue}{+5x }
& = & -2 \color{blue}{+11} \\\Leftrightarrow &8x
& = &9\\\Leftrightarrow & \color{red}{8}x
& = &9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)