Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-10x+13=4+x\)
- \(-13x+4=6+7x\)
- \(-x-9=-12+15x\)
- \(-2x+11=-8+x\)
- \(-6x-1=-12+x\)
- \(2x-8=-10+7x\)
- \(12x-3=-2+7x\)
- \(13x+12=10+5x\)
- \(11x-9=-8-10x\)
- \(-5x-11=15+3x\)
- \(8x-3=9+3x\)
- \(11x-3=1+4x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -10x \color{red}{+13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x }
& = & 4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 4 \color{blue}{-13} \\\Leftrightarrow &-11x
& = &-9\\\Leftrightarrow & \color{red}{-11}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+4}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-7x }
& = & 6 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -13x \color{blue}{-7x }
& = & 6 \color{blue}{-4} \\\Leftrightarrow &-20x
& = &2\\\Leftrightarrow & \color{red}{-20}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{2}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-9}& = & -12 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9-15x }
& = & -12 \color{red}{ +15x }\color{blue}{+9-15x } \\\Leftrightarrow & -x \color{blue}{-15x }
& = & -12 \color{blue}{+9} \\\Leftrightarrow &-16x
& = &-3\\\Leftrightarrow & \color{red}{-16}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-x }
& = & -8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & -8 \color{blue}{-11} \\\Leftrightarrow &-3x
& = &-19\\\Leftrightarrow & \color{red}{-3}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-19}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{19}{3} } & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1-x }
& = & -12 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -12 \color{blue}{+1} \\\Leftrightarrow &-7x
& = &-11\\\Leftrightarrow & \color{red}{-7}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-8}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-7x }
& = & -10 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 2x \color{blue}{-7x }
& = & -10 \color{blue}{+8} \\\Leftrightarrow &-5x
& = &-2\\\Leftrightarrow & \color{red}{-5}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-3}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-7x }
& = & -2 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & 12x \color{blue}{-7x }
& = & -2 \color{blue}{+3} \\\Leftrightarrow &5x
& = &1\\\Leftrightarrow & \color{red}{5}x
& = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+12}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12-5x }
& = & 10 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & 13x \color{blue}{-5x }
& = & 10 \color{blue}{-12} \\\Leftrightarrow &8x
& = &-2\\\Leftrightarrow & \color{red}{8}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{-2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-9}& = & -8 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9+10x }
& = & -8 \color{red}{ -10x }\color{blue}{+9+10x } \\\Leftrightarrow & 11x \color{blue}{+10x }
& = & -8 \color{blue}{+9} \\\Leftrightarrow &21x
& = &1\\\Leftrightarrow & \color{red}{21}x
& = &1\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}}
& = & \frac{1}{21} \\\Leftrightarrow & \color{green}{ x = \frac{1}{21} } & & \\ & V = \left\{ \frac{1}{21} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-11}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-3x }
& = & 15 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & -5x \color{blue}{-3x }
& = & 15 \color{blue}{+11} \\\Leftrightarrow &-8x
& = &26\\\Leftrightarrow & \color{red}{-8}x
& = &26\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{26}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{4} } & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-3}& = & 9 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3-3x }
& = & 9 \color{red}{ +3x }\color{blue}{+3-3x } \\\Leftrightarrow & 8x \color{blue}{-3x }
& = & 9 \color{blue}{+3} \\\Leftrightarrow &5x
& = &12\\\Leftrightarrow & \color{red}{5}x
& = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-3}& = & 1 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3-4x }
& = & 1 \color{red}{ +4x }\color{blue}{+3-4x } \\\Leftrightarrow & 11x \color{blue}{-4x }
& = & 1 \color{blue}{+3} \\\Leftrightarrow &7x
& = &4\\\Leftrightarrow & \color{red}{7}x
& = &4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)