Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-9x+7=14+x\)
- \(14x-2=12+9x\)
- \(-14x-1=7+x\)
- \(10x-7=-5+7x\)
- \(12x-11=3+x\)
- \(-4x-4=-3+x\)
- \(-11x-11=14+x\)
- \(-5x+12=11+x\)
- \(-x+6=12+x\)
- \(7x-8=-8-2x\)
- \(13x-12=-8-3x\)
- \(8x-7=14+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -9x \color{red}{+7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-x }
& = & 14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 14 \color{blue}{-7} \\\Leftrightarrow &-10x
& = &7\\\Leftrightarrow & \color{red}{-10}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-2}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2-9x }
& = & 12 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & 14x \color{blue}{-9x }
& = & 12 \color{blue}{+2} \\\Leftrightarrow &5x
& = &14\\\Leftrightarrow & \color{red}{5}x
& = &14\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{14}{5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-1}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x }
& = & 7 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 7 \color{blue}{+1} \\\Leftrightarrow &-15x
& = &8\\\Leftrightarrow & \color{red}{-15}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-7}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7-7x }
& = & -5 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & 10x \color{blue}{-7x }
& = & -5 \color{blue}{+7} \\\Leftrightarrow &3x
& = &2\\\Leftrightarrow & \color{red}{3}x
& = &2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11-x }
& = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & 3 \color{blue}{+11} \\\Leftrightarrow &11x
& = &14\\\Leftrightarrow & \color{red}{11}x
& = &14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{14}{11} } & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-x }
& = & -3 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -3 \color{blue}{+4} \\\Leftrightarrow &-5x
& = &1\\\Leftrightarrow & \color{red}{-5}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-11}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-x }
& = & 14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 14 \color{blue}{+11} \\\Leftrightarrow &-12x
& = &25\\\Leftrightarrow & \color{red}{-12}x
& = &25\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{25}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{12} } & & \\ & V = \left\{ \frac{-25}{12} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+12}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-x }
& = & 11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 11 \color{blue}{-12} \\\Leftrightarrow &-6x
& = &-1\\\Leftrightarrow & \color{red}{-6}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+6}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6-x }
& = & 12 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -x \color{blue}{-x }
& = & 12 \color{blue}{-6} \\\Leftrightarrow &-2x
& = &6\\\Leftrightarrow & \color{red}{-2}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}}
& = & \frac{6}{-2} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-8}& = & -8 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8+2x }
& = & -8 \color{red}{ -2x }\color{blue}{+8+2x } \\\Leftrightarrow & 7x \color{blue}{+2x }
& = & -8 \color{blue}{+8} \\\Leftrightarrow &9x
& = &0\\\Leftrightarrow & \color{red}{9}x
& = &0\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{0}{9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-12}& = & -8 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12+3x }
& = & -8 \color{red}{ -3x }\color{blue}{+12+3x } \\\Leftrightarrow & 13x \color{blue}{+3x }
& = & -8 \color{blue}{+12} \\\Leftrightarrow &16x
& = &4\\\Leftrightarrow & \color{red}{16}x
& = &4\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}}
& = & \frac{4}{16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7-x }
& = & 14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 8x \color{blue}{-x }
& = & 14 \color{blue}{+7} \\\Leftrightarrow &7x
& = &21\\\Leftrightarrow & \color{red}{7}x
& = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)