Bepaal de waarde van x.
- \(3x+14=14\)
- \(2x-10=6\)
- \(-10x+11=-6\)
- \(4x-15=15\)
- \(-13x-10=15\)
- \(15x-5=2\)
- \(7x-2=8\)
- \(-12x+13=-5\)
- \(11x+5=-8\)
- \(-13x+15=-11\)
- \(-2x+6=-8\)
- \(-7x+15=15\)
Bepaal de waarde van x.
Verbetersleutel
- \(\begin{align} & 3x \color{red}{+14}& = &14 \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14}
& = &14\color{blue}{-14} \\\Leftrightarrow &3x
& = &0\\\Leftrightarrow & \color{red}{3}x
& = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3}
& = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-10}& = &6 \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10}
& = &6\color{blue}{+10} \\\Leftrightarrow &2x
& = &16\\\Leftrightarrow & \color{red}{2}x
& = &16\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2}
& = & \frac{16}{2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+11}& = &-6 \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11}
& = &-6\color{blue}{-11} \\\Leftrightarrow &-10x
& = &-17\\\Leftrightarrow & \color{red}{-10}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10}
& = & \frac{-17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{17}{10} } & & \\ & V = \left\{ \frac{17}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-15}& = &15 \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15}
& = &15\color{blue}{+15} \\\Leftrightarrow &4x
& = &30\\\Leftrightarrow & \color{red}{4}x
& = &30\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4}
& = & \frac{30}{4} \\\Leftrightarrow & \color{green}{ x = \frac{15}{2} } & & \\ & V = \left\{ \frac{15}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-10}& = &15 \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10}
& = &15\color{blue}{+10} \\\Leftrightarrow &-13x
& = &25\\\Leftrightarrow & \color{red}{-13}x
& = &25\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13}
& = & \frac{25}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{13} } & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-5}& = &2 \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5}
& = &2\color{blue}{+5} \\\Leftrightarrow &15x
& = &7\\\Leftrightarrow & \color{red}{15}x
& = &7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15}
& = & \frac{7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-2}& = &8 \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2}
& = &8\color{blue}{+2} \\\Leftrightarrow &7x
& = &10\\\Leftrightarrow & \color{red}{7}x
& = &10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7}
& = & \frac{10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+13}& = &-5 \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13}
& = &-5\color{blue}{-13} \\\Leftrightarrow &-12x
& = &-18\\\Leftrightarrow & \color{red}{-12}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12}
& = & \frac{-18}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+5}& = &-8 \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5}
& = &-8\color{blue}{-5} \\\Leftrightarrow &11x
& = &-13\\\Leftrightarrow & \color{red}{11}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11}
& = & \frac{-13}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+15}& = &-11 \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15}
& = &-11\color{blue}{-15} \\\Leftrightarrow &-13x
& = &-26\\\Leftrightarrow & \color{red}{-13}x
& = &-26\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13}
& = & \frac{-26}{-13} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+6}& = &-8 \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6}
& = &-8\color{blue}{-6} \\\Leftrightarrow &-2x
& = &-14\\\Leftrightarrow & \color{red}{-2}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2}
& = & \frac{-14}{-2} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+15}& = &15 \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15}
& = &15\color{blue}{-15} \\\Leftrightarrow &-7x
& = &0\\\Leftrightarrow & \color{red}{-7}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7}
& = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)