Bepaal de waarde van x.
- \(x+4=5\)
- \(-7x+12=12\)
- \(3x-4=10\)
- \(-15x-4=-12\)
- \(8x+3=11\)
- \(3x-14=13\)
- \(-3x-15=6\)
- \(x+13=14\)
- \(-11x-7=11\)
- \(-5x-3=-4\)
- \(-3x-10=6\)
- \(9x-8=4\)
Bepaal de waarde van x.
Verbetersleutel
- \(\begin{align} & x \color{red}{+4}& = &5 \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4}
& = &5\color{blue}{-4} \\\Leftrightarrow &x
& = &1\\\Leftrightarrow & \color{red}{}x
& = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1}
& = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+12}& = &12 \\\Leftrightarrow & -7x \color{red}{+12}\color{blue}{-12}
& = &12\color{blue}{-12} \\\Leftrightarrow &-7x
& = &0\\\Leftrightarrow & \color{red}{-7}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7}
& = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-4}& = &10 \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4}
& = &10\color{blue}{+4} \\\Leftrightarrow &3x
& = &14\\\Leftrightarrow & \color{red}{3}x
& = &14\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3}
& = & \frac{14}{3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-4}& = &-12 \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4}
& = &-12\color{blue}{+4} \\\Leftrightarrow &-15x
& = &-8\\\Leftrightarrow & \color{red}{-15}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15}
& = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+3}& = &11 \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3}
& = &11\color{blue}{-3} \\\Leftrightarrow &8x
& = &8\\\Leftrightarrow & \color{red}{8}x
& = &8\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8}
& = & \frac{8}{8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-14}& = &13 \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14}
& = &13\color{blue}{+14} \\\Leftrightarrow &3x
& = &27\\\Leftrightarrow & \color{red}{3}x
& = &27\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3}
& = & \frac{27}{3} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-15}& = &6 \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15}
& = &6\color{blue}{+15} \\\Leftrightarrow &-3x
& = &21\\\Leftrightarrow & \color{red}{-3}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3}
& = & \frac{21}{-3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+13}& = &14 \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13}
& = &14\color{blue}{-13} \\\Leftrightarrow &x
& = &1\\\Leftrightarrow & \color{red}{}x
& = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1}
& = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-7}& = &11 \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7}
& = &11\color{blue}{+7} \\\Leftrightarrow &-11x
& = &18\\\Leftrightarrow & \color{red}{-11}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11}
& = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-3}& = &-4 \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3}
& = &-4\color{blue}{+3} \\\Leftrightarrow &-5x
& = &-1\\\Leftrightarrow & \color{red}{-5}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5}
& = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-10}& = &6 \\\Leftrightarrow & -3x \color{red}{-10}\color{blue}{+10}
& = &6\color{blue}{+10} \\\Leftrightarrow &-3x
& = &16\\\Leftrightarrow & \color{red}{-3}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3}
& = & \frac{16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-8}& = &4 \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8}
& = &4\color{blue}{+8} \\\Leftrightarrow &9x
& = &12\\\Leftrightarrow & \color{red}{9}x
& = &12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9}
& = & \frac{12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)