Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-12x+3=-7+x\)
- \(12x-9=-6+x\)
- \(7x-15=-14-10x\)
- \(2x+7=10+3x\)
- \(-14x-11=12+x\)
- \(-15x+10=15+13x\)
- \(-9x+15=-8+x\)
- \(-6x-5=13+x\)
- \(-12x+5=-8+13x\)
- \(6x+1=-7+x\)
- \(-7x-2=7+x\)
- \(10x-8=4+3x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -12x \color{red}{+3}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-x }
& = & -7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -7 \color{blue}{-3} \\\Leftrightarrow &-13x
& = &-10\\\Leftrightarrow & \color{red}{-13}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-9}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9-x }
& = & -6 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & -6 \color{blue}{+9} \\\Leftrightarrow &11x
& = &3\\\Leftrightarrow & \color{red}{11}x
& = &3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-15}& = & -14 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+10x }
& = & -14 \color{red}{ -10x }\color{blue}{+15+10x } \\\Leftrightarrow & 7x \color{blue}{+10x }
& = & -14 \color{blue}{+15} \\\Leftrightarrow &17x
& = &1\\\Leftrightarrow & \color{red}{17}x
& = &1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+7}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-3x }
& = & 10 \color{red}{ +3x }\color{blue}{-7-3x } \\\Leftrightarrow & 2x \color{blue}{-3x }
& = & 10 \color{blue}{-7} \\\Leftrightarrow &-x
& = &3\\\Leftrightarrow & \color{red}{-}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-x }
& = & 12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 12 \color{blue}{+11} \\\Leftrightarrow &-15x
& = &23\\\Leftrightarrow & \color{red}{-15}x
& = &23\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{23}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{15} } & & \\ & V = \left\{ \frac{-23}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+10}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-13x }
& = & 15 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & 15 \color{blue}{-10} \\\Leftrightarrow &-28x
& = &5\\\Leftrightarrow & \color{red}{-28}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{5}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{28} } & & \\ & V = \left\{ \frac{-5}{28} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-x }
& = & -8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -8 \color{blue}{-15} \\\Leftrightarrow &-10x
& = &-23\\\Leftrightarrow & \color{red}{-10}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-23}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{23}{10} } & & \\ & V = \left\{ \frac{23}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-x }
& = & 13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & 13 \color{blue}{+5} \\\Leftrightarrow &-7x
& = &18\\\Leftrightarrow & \color{red}{-7}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+5}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+5}\color{blue}{-5-13x }
& = & -8 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & -8 \color{blue}{-5} \\\Leftrightarrow &-25x
& = &-13\\\Leftrightarrow & \color{red}{-25}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-13}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{13}{25} } & & \\ & V = \left\{ \frac{13}{25} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+1}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1-x }
& = & -7 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & -7 \color{blue}{-1} \\\Leftrightarrow &5x
& = &-8\\\Leftrightarrow & \color{red}{5}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-2}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x }
& = & 7 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & 7 \color{blue}{+2} \\\Leftrightarrow &-8x
& = &9\\\Leftrightarrow & \color{red}{-8}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-8}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8-3x }
& = & 4 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & 10x \color{blue}{-3x }
& = & 4 \color{blue}{+8} \\\Leftrightarrow &7x
& = &12\\\Leftrightarrow & \color{red}{7}x
& = &12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)