Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(12x-3=-15-11x\)
- \(-10x-2=8+x\)
- \(12x+3=13+x\)
- \(2x-6=10+x\)
- \(-12x-5=2+x\)
- \(11x+4=3-2x\)
- \(-6x-6=-9+7x\)
- \(-14x+6=-12+x\)
- \(-7x-6=-11+x\)
- \(-5x+6=8+x\)
- \(-10x+7=-6+7x\)
- \(-8x-14=-7+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 12x \color{red}{-3}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3+11x }
& = & -15 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & -15 \color{blue}{+3} \\\Leftrightarrow &23x
& = &-12\\\Leftrightarrow & \color{red}{23}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-12}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{23} } & & \\ & V = \left\{ \frac{-12}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-2}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-x }
& = & 8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 8 \color{blue}{+2} \\\Leftrightarrow &-11x
& = &10\\\Leftrightarrow & \color{red}{-11}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3-x }
& = & 13 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & 13 \color{blue}{-3} \\\Leftrightarrow &11x
& = &10\\\Leftrightarrow & \color{red}{11}x
& = &10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-x }
& = & 10 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & 10 \color{blue}{+6} \\\Leftrightarrow &x
& = &16\\\Leftrightarrow & \color{red}{}x
& = &16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 16 \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x }
& = & 2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 2 \color{blue}{+5} \\\Leftrightarrow &-13x
& = &7\\\Leftrightarrow & \color{red}{-13}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+4}& = & 3 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4+2x }
& = & 3 \color{red}{ -2x }\color{blue}{-4+2x } \\\Leftrightarrow & 11x \color{blue}{+2x }
& = & 3 \color{blue}{-4} \\\Leftrightarrow &13x
& = &-1\\\Leftrightarrow & \color{red}{13}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-6}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-7x }
& = & -9 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & -9 \color{blue}{+6} \\\Leftrightarrow &-13x
& = &-3\\\Leftrightarrow & \color{red}{-13}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+6}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+6}\color{blue}{-6-x }
& = & -12 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -12 \color{blue}{-6} \\\Leftrightarrow &-15x
& = &-18\\\Leftrightarrow & \color{red}{-15}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-6}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-x }
& = & -11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -11 \color{blue}{+6} \\\Leftrightarrow &-8x
& = &-5\\\Leftrightarrow & \color{red}{-8}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+6}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-x }
& = & 8 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 8 \color{blue}{-6} \\\Leftrightarrow &-6x
& = &2\\\Leftrightarrow & \color{red}{-6}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+7}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-7x }
& = & -6 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & -10x \color{blue}{-7x }
& = & -6 \color{blue}{-7} \\\Leftrightarrow &-17x
& = &-13\\\Leftrightarrow & \color{red}{-17}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-13}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x }
& = & -7 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & -7 \color{blue}{+14} \\\Leftrightarrow &-9x
& = &7\\\Leftrightarrow & \color{red}{-9}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)