Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(2x-3=-10+7x\)
- \(13x+10=-13-4x\)
- \(7x+5=-11+3x\)
- \(-4x+7=7+5x\)
- \(12x-12=-5+11x\)
- \(-6x+15=-1+13x\)
- \(x-8=-15+13x\)
- \(-14x+10=-5+x\)
- \(-7x+5=-15+11x\)
- \(x+11=-2-7x\)
- \(-2x+3=4+7x\)
- \(-6x+10=1+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 2x \color{red}{-3}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-7x }
& = & -10 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & 2x \color{blue}{-7x }
& = & -10 \color{blue}{+3} \\\Leftrightarrow &-5x
& = &-7\\\Leftrightarrow & \color{red}{-5}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+10}& = & -13 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10+4x }
& = & -13 \color{red}{ -4x }\color{blue}{-10+4x } \\\Leftrightarrow & 13x \color{blue}{+4x }
& = & -13 \color{blue}{-10} \\\Leftrightarrow &17x
& = &-23\\\Leftrightarrow & \color{red}{17}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-23}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{17} } & & \\ & V = \left\{ \frac{-23}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+5}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5-3x }
& = & -11 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & 7x \color{blue}{-3x }
& = & -11 \color{blue}{-5} \\\Leftrightarrow &4x
& = &-16\\\Leftrightarrow & \color{red}{4}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{-16}{4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+7}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-5x }
& = & 7 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -4x \color{blue}{-5x }
& = & 7 \color{blue}{-7} \\\Leftrightarrow &-9x
& = &0\\\Leftrightarrow & \color{red}{-9}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-12}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12-11x }
& = & -5 \color{red}{ +11x }\color{blue}{+12-11x } \\\Leftrightarrow & 12x \color{blue}{-11x }
& = & -5 \color{blue}{+12} \\\Leftrightarrow &x
& = &7\\\Leftrightarrow & \color{red}{}x
& = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+15}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15-13x }
& = & -1 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & -1 \color{blue}{-15} \\\Leftrightarrow &-19x
& = &-16\\\Leftrightarrow & \color{red}{-19}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-16}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{16}{19} } & & \\ & V = \left\{ \frac{16}{19} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-8}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8-13x }
& = & -15 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & x \color{blue}{-13x }
& = & -15 \color{blue}{+8} \\\Leftrightarrow &-12x
& = &-7\\\Leftrightarrow & \color{red}{-12}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+10}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-x }
& = & -5 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -5 \color{blue}{-10} \\\Leftrightarrow &-15x
& = &-15\\\Leftrightarrow & \color{red}{-15}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-15}{-15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+5}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-11x }
& = & -15 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & -7x \color{blue}{-11x }
& = & -15 \color{blue}{-5} \\\Leftrightarrow &-18x
& = &-20\\\Leftrightarrow & \color{red}{-18}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}}
& = & \frac{-20}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+11}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{+11}\color{blue}{-11+7x }
& = & -2 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & x \color{blue}{+7x }
& = & -2 \color{blue}{-11} \\\Leftrightarrow &8x
& = &-13\\\Leftrightarrow & \color{red}{8}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{-13}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+3}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3-7x }
& = & 4 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -2x \color{blue}{-7x }
& = & 4 \color{blue}{-3} \\\Leftrightarrow &-9x
& = &1\\\Leftrightarrow & \color{red}{-9}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10-x }
& = & 1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & 1 \color{blue}{-10} \\\Leftrightarrow &-7x
& = &-9\\\Leftrightarrow & \color{red}{-7}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)