Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(x-12=4+9x\)
- \(9x-15=-7-11x\)
- \(-6x+7=14+x\)
- \(11x-14=13-5x\)
- \(-5x+14=12+x\)
- \(-4x-15=-13+x\)
- \(-15x+5=14+x\)
- \(11x-14=-10+7x\)
- \(7x+3=-8+2x\)
- \(13x-7=-3+5x\)
- \(-3x+12=-11+x\)
- \(x+9=11-11x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & x \color{red}{-12}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12-9x }
& = & 4 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & x \color{blue}{-9x }
& = & 4 \color{blue}{+12} \\\Leftrightarrow &-8x
& = &16\\\Leftrightarrow & \color{red}{-8}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{16}{-8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-15}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15+11x }
& = & -7 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 9x \color{blue}{+11x }
& = & -7 \color{blue}{+15} \\\Leftrightarrow &20x
& = &8\\\Leftrightarrow & \color{red}{20}x
& = &8\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{8}{20} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7-x }
& = & 14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & 14 \color{blue}{-7} \\\Leftrightarrow &-7x
& = &7\\\Leftrightarrow & \color{red}{-7}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-14}& = & 13 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14+5x }
& = & 13 \color{red}{ -5x }\color{blue}{+14+5x } \\\Leftrightarrow & 11x \color{blue}{+5x }
& = & 13 \color{blue}{+14} \\\Leftrightarrow &16x
& = &27\\\Leftrightarrow & \color{red}{16}x
& = &27\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}}
& = & \frac{27}{16} \\\Leftrightarrow & \color{green}{ x = \frac{27}{16} } & & \\ & V = \left\{ \frac{27}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+14}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-x }
& = & 12 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 12 \color{blue}{-14} \\\Leftrightarrow &-6x
& = &-2\\\Leftrightarrow & \color{red}{-6}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-15}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-x }
& = & -13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -13 \color{blue}{+15} \\\Leftrightarrow &-5x
& = &2\\\Leftrightarrow & \color{red}{-5}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+5}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-x }
& = & 14 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & 14 \color{blue}{-5} \\\Leftrightarrow &-16x
& = &9\\\Leftrightarrow & \color{red}{-16}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{9}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{16} } & & \\ & V = \left\{ \frac{-9}{16} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-14}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14-7x }
& = & -10 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 11x \color{blue}{-7x }
& = & -10 \color{blue}{+14} \\\Leftrightarrow &4x
& = &4\\\Leftrightarrow & \color{red}{4}x
& = &4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{4}{4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+3}& = & -8 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3-2x }
& = & -8 \color{red}{ +2x }\color{blue}{-3-2x } \\\Leftrightarrow & 7x \color{blue}{-2x }
& = & -8 \color{blue}{-3} \\\Leftrightarrow &5x
& = &-11\\\Leftrightarrow & \color{red}{5}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-7}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7-5x }
& = & -3 \color{red}{ +5x }\color{blue}{+7-5x } \\\Leftrightarrow & 13x \color{blue}{-5x }
& = & -3 \color{blue}{+7} \\\Leftrightarrow &8x
& = &4\\\Leftrightarrow & \color{red}{8}x
& = &4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+12}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12-x }
& = & -11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -11 \color{blue}{-12} \\\Leftrightarrow &-4x
& = &-23\\\Leftrightarrow & \color{red}{-4}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-23}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{23}{4} } & & \\ & V = \left\{ \frac{23}{4} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+9}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9+11x }
& = & 11 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & x \color{blue}{+11x }
& = & 11 \color{blue}{-9} \\\Leftrightarrow &12x
& = &2\\\Leftrightarrow & \color{red}{12}x
& = &2\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}}
& = & \frac{2}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)