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