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