Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-13x-9=9+x\)
- \(11x+4=2-13x\)
- \(6x-1=-6+x\)
- \(12x-15=13-11x\)
- \(14x-13=-5-13x\)
- \(-4x-11=-8+x\)
- \(-7x-3=7+11x\)
- \(11x-13=12-5x\)
- \(3x+2=-15+4x\)
- \(9x-2=-10-11x\)
- \(3x-4=-7+13x\)
- \(5x+10=-4+11x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -13x \color{red}{-9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-x }
& = & 9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 9 \color{blue}{+9} \\\Leftrightarrow &-14x
& = &18\\\Leftrightarrow & \color{red}{-14}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+4}& = & 2 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4+13x }
& = & 2 \color{red}{ -13x }\color{blue}{-4+13x } \\\Leftrightarrow & 11x \color{blue}{+13x }
& = & 2 \color{blue}{-4} \\\Leftrightarrow &24x
& = &-2\\\Leftrightarrow & \color{red}{24}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}}
& = & \frac{-2}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1-x }
& = & -6 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & -6 \color{blue}{+1} \\\Leftrightarrow &5x
& = &-5\\\Leftrightarrow & \color{red}{5}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-15}& = & 13 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15+11x }
& = & 13 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & 13 \color{blue}{+15} \\\Leftrightarrow &23x
& = &28\\\Leftrightarrow & \color{red}{23}x
& = &28\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{28}{23} \\\Leftrightarrow & \color{green}{ x = \frac{28}{23} } & & \\ & V = \left\{ \frac{28}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-13}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13+13x }
& = & -5 \color{red}{ -13x }\color{blue}{+13+13x } \\\Leftrightarrow & 14x \color{blue}{+13x }
& = & -5 \color{blue}{+13} \\\Leftrightarrow &27x
& = &8\\\Leftrightarrow & \color{red}{27}x
& = &8\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}}
& = & \frac{8}{27} \\\Leftrightarrow & \color{green}{ x = \frac{8}{27} } & & \\ & V = \left\{ \frac{8}{27} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-x }
& = & -8 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -8 \color{blue}{+11} \\\Leftrightarrow &-5x
& = &3\\\Leftrightarrow & \color{red}{-5}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-3}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-11x }
& = & 7 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & -7x \color{blue}{-11x }
& = & 7 \color{blue}{+3} \\\Leftrightarrow &-18x
& = &10\\\Leftrightarrow & \color{red}{-18}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}}
& = & \frac{10}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-13}& = & 12 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13+5x }
& = & 12 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 11x \color{blue}{+5x }
& = & 12 \color{blue}{+13} \\\Leftrightarrow &16x
& = &25\\\Leftrightarrow & \color{red}{16}x
& = &25\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}}
& = & \frac{25}{16} \\\Leftrightarrow & \color{green}{ x = \frac{25}{16} } & & \\ & V = \left\{ \frac{25}{16} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+2}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2-4x }
& = & -15 \color{red}{ +4x }\color{blue}{-2-4x } \\\Leftrightarrow & 3x \color{blue}{-4x }
& = & -15 \color{blue}{-2} \\\Leftrightarrow &-x
& = &-17\\\Leftrightarrow & \color{red}{-}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-17}{-1} \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-2}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2+11x }
& = & -10 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 9x \color{blue}{+11x }
& = & -10 \color{blue}{+2} \\\Leftrightarrow &20x
& = &-8\\\Leftrightarrow & \color{red}{20}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{-8}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-4}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4-13x }
& = & -7 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & 3x \color{blue}{-13x }
& = & -7 \color{blue}{+4} \\\Leftrightarrow &-10x
& = &-3\\\Leftrightarrow & \color{red}{-10}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+10}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10-11x }
& = & -4 \color{red}{ +11x }\color{blue}{-10-11x } \\\Leftrightarrow & 5x \color{blue}{-11x }
& = & -4 \color{blue}{-10} \\\Leftrightarrow &-6x
& = &-14\\\Leftrightarrow & \color{red}{-6}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)