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