Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(4x-8=10-7x\)
- \(2x+1=-7+x\)
- \(-6x-12=-11+x\)
- \(11x-10=-6-13x\)
- \(13x+7=14+14x\)
- \(-8x-1=2+x\)
- \(-12x-10=-7+x\)
- \(-4x+1=7+9x\)
- \(8x-11=9+x\)
- \(-15x-5=-3+x\)
- \(-15x+14=7+x\)
- \(6x-8=-13+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 4x \color{red}{-8}& = & 10 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8+7x }
& = & 10 \color{red}{ -7x }\color{blue}{+8+7x } \\\Leftrightarrow & 4x \color{blue}{+7x }
& = & 10 \color{blue}{+8} \\\Leftrightarrow &11x
& = &18\\\Leftrightarrow & \color{red}{11}x
& = &18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+1}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1-x }
& = & -7 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & -7 \color{blue}{-1} \\\Leftrightarrow &x
& = &-8\\\Leftrightarrow & \color{red}{}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-12}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-x }
& = & -11 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -11 \color{blue}{+12} \\\Leftrightarrow &-7x
& = &1\\\Leftrightarrow & \color{red}{-7}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-10}& = & -6 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10+13x }
& = & -6 \color{red}{ -13x }\color{blue}{+10+13x } \\\Leftrightarrow & 11x \color{blue}{+13x }
& = & -6 \color{blue}{+10} \\\Leftrightarrow &24x
& = &4\\\Leftrightarrow & \color{red}{24}x
& = &4\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}}
& = & \frac{4}{24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+7}& = & 14 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7-14x }
& = & 14 \color{red}{ +14x }\color{blue}{-7-14x } \\\Leftrightarrow & 13x \color{blue}{-14x }
& = & 14 \color{blue}{-7} \\\Leftrightarrow &-x
& = &7\\\Leftrightarrow & \color{red}{-}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-x }
& = & 2 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 2 \color{blue}{+1} \\\Leftrightarrow &-9x
& = &3\\\Leftrightarrow & \color{red}{-9}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-10}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-x }
& = & -7 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -7 \color{blue}{+10} \\\Leftrightarrow &-13x
& = &3\\\Leftrightarrow & \color{red}{-13}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+1}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-9x }
& = & 7 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & -4x \color{blue}{-9x }
& = & 7 \color{blue}{-1} \\\Leftrightarrow &-13x
& = &6\\\Leftrightarrow & \color{red}{-13}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-11}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11-x }
& = & 9 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 8x \color{blue}{-x }
& = & 9 \color{blue}{+11} \\\Leftrightarrow &7x
& = &20\\\Leftrightarrow & \color{red}{7}x
& = &20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{20}{7} } & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-5}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5-x }
& = & -3 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & -3 \color{blue}{+5} \\\Leftrightarrow &-16x
& = &2\\\Leftrightarrow & \color{red}{-16}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-x }
& = & 7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & 7 \color{blue}{-14} \\\Leftrightarrow &-16x
& = &-7\\\Leftrightarrow & \color{red}{-16}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-8}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8-x }
& = & -13 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & -13 \color{blue}{+8} \\\Leftrightarrow &5x
& = &-5\\\Leftrightarrow & \color{red}{5}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)