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