Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-6x-15=-11+x\)
- \(11x+2=-5+12x\)
- \(-4x-14=9+x\)
- \(-7x+5=5+x\)
- \(14x-8=-6-13x\)
- \(-15x-2=-7+13x\)
- \(8x-11=10-7x\)
- \(8x-14=7+x\)
- \(10x+5=-3-9x\)
- \(13x-1=9+11x\)
- \(-9x+6=10+5x\)
- \(7x+11=2+11x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -6x \color{red}{-15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-x }
& = & -11 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -11 \color{blue}{+15} \\\Leftrightarrow &-7x
& = &4\\\Leftrightarrow & \color{red}{-7}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+2}& = & -5 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2-12x }
& = & -5 \color{red}{ +12x }\color{blue}{-2-12x } \\\Leftrightarrow & 11x \color{blue}{-12x }
& = & -5 \color{blue}{-2} \\\Leftrightarrow &-x
& = &-7\\\Leftrightarrow & \color{red}{-}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-14}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14-x }
& = & 9 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & 9 \color{blue}{+14} \\\Leftrightarrow &-5x
& = &23\\\Leftrightarrow & \color{red}{-5}x
& = &23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{5} } & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+5}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-x }
& = & 5 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & 5 \color{blue}{-5} \\\Leftrightarrow &-8x
& = &0\\\Leftrightarrow & \color{red}{-8}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{0}{-8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-8}& = & -6 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8+13x }
& = & -6 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & 14x \color{blue}{+13x }
& = & -6 \color{blue}{+8} \\\Leftrightarrow &27x
& = &2\\\Leftrightarrow & \color{red}{27}x
& = &2\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}}
& = & \frac{2}{27} \\\Leftrightarrow & \color{green}{ x = \frac{2}{27} } & & \\ & V = \left\{ \frac{2}{27} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-2}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-13x }
& = & -7 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & -7 \color{blue}{+2} \\\Leftrightarrow &-28x
& = &-5\\\Leftrightarrow & \color{red}{-28}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{-5}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{5}{28} } & & \\ & V = \left\{ \frac{5}{28} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-11}& = & 10 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11+7x }
& = & 10 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & 8x \color{blue}{+7x }
& = & 10 \color{blue}{+11} \\\Leftrightarrow &15x
& = &21\\\Leftrightarrow & \color{red}{15}x
& = &21\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{21}{15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14-x }
& = & 7 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 8x \color{blue}{-x }
& = & 7 \color{blue}{+14} \\\Leftrightarrow &7x
& = &21\\\Leftrightarrow & \color{red}{7}x
& = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+5}& = & -3 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5+9x }
& = & -3 \color{red}{ -9x }\color{blue}{-5+9x } \\\Leftrightarrow & 10x \color{blue}{+9x }
& = & -3 \color{blue}{-5} \\\Leftrightarrow &19x
& = &-8\\\Leftrightarrow & \color{red}{19}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-8}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-1}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1-11x }
& = & 9 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & 13x \color{blue}{-11x }
& = & 9 \color{blue}{+1} \\\Leftrightarrow &2x
& = &10\\\Leftrightarrow & \color{red}{2}x
& = &10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{10}{2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+6}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-5x }
& = & 10 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & -9x \color{blue}{-5x }
& = & 10 \color{blue}{-6} \\\Leftrightarrow &-14x
& = &4\\\Leftrightarrow & \color{red}{-14}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+11}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11-11x }
& = & 2 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 7x \color{blue}{-11x }
& = & 2 \color{blue}{-11} \\\Leftrightarrow &-4x
& = &-9\\\Leftrightarrow & \color{red}{-4}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)