Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-6x+14=14+7x\)
- \(6x+4=7+x\)
- \(-13x-11=-7+x\)
- \(x-10=7+2x\)
- \(-2x+10=3+3x\)
- \(-3x-2=-9+10x\)
- \(-9x-9=-13+x\)
- \(x+5=-1+8x\)
- \(-6x+4=-11+x\)
- \(-7x-9=12+x\)
- \(6x-4=3-11x\)
- \(14x+9=-4+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -6x \color{red}{+14}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-7x }
& = & 14 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & 14 \color{blue}{-14} \\\Leftrightarrow &-13x
& = &0\\\Leftrightarrow & \color{red}{-13}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+4}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4-x }
& = & 7 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & 7 \color{blue}{-4} \\\Leftrightarrow &5x
& = &3\\\Leftrightarrow & \color{red}{5}x
& = &3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-11}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-11}\color{blue}{+11-x }
& = & -7 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -7 \color{blue}{+11} \\\Leftrightarrow &-14x
& = &4\\\Leftrightarrow & \color{red}{-14}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-10}& = & 7 \color{red}{ +2x } \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10-2x }
& = & 7 \color{red}{ +2x }\color{blue}{+10-2x } \\\Leftrightarrow & x \color{blue}{-2x }
& = & 7 \color{blue}{+10} \\\Leftrightarrow &-x
& = &17\\\Leftrightarrow & \color{red}{-}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{17}{-1} \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+10}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-3x }
& = & 3 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & -2x \color{blue}{-3x }
& = & 3 \color{blue}{-10} \\\Leftrightarrow &-5x
& = &-7\\\Leftrightarrow & \color{red}{-5}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-2}& = & -9 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2-10x }
& = & -9 \color{red}{ +10x }\color{blue}{+2-10x } \\\Leftrightarrow & -3x \color{blue}{-10x }
& = & -9 \color{blue}{+2} \\\Leftrightarrow &-13x
& = &-7\\\Leftrightarrow & \color{red}{-13}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-x }
& = & -13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -13 \color{blue}{+9} \\\Leftrightarrow &-10x
& = &-4\\\Leftrightarrow & \color{red}{-10}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+5}& = & -1 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5-8x }
& = & -1 \color{red}{ +8x }\color{blue}{-5-8x } \\\Leftrightarrow & x \color{blue}{-8x }
& = & -1 \color{blue}{-5} \\\Leftrightarrow &-7x
& = &-6\\\Leftrightarrow & \color{red}{-7}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+4}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-x }
& = & -11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -11 \color{blue}{-4} \\\Leftrightarrow &-7x
& = &-15\\\Leftrightarrow & \color{red}{-7}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-15}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{15}{7} } & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-9}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-9}\color{blue}{+9-x }
& = & 12 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & 12 \color{blue}{+9} \\\Leftrightarrow &-8x
& = &21\\\Leftrightarrow & \color{red}{-8}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{21}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{8} } & & \\ & V = \left\{ \frac{-21}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-4}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4+11x }
& = & 3 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & 3 \color{blue}{+4} \\\Leftrightarrow &17x
& = &7\\\Leftrightarrow & \color{red}{17}x
& = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+9}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9-x }
& = & -4 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & -4 \color{blue}{-9} \\\Leftrightarrow &13x
& = &-13\\\Leftrightarrow & \color{red}{13}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)