Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(15x-12=12-14x\)
- \(5x+3=2-14x\)
- \(-5x-8=-3+3x\)
- \(-5x+11=4+x\)
- \(-3x+13=13+13x\)
- \(-8x-13=-14+9x\)
- \(-6x-5=-5+x\)
- \(3x-8=2-2x\)
- \(10x+2=10+7x\)
- \(14x+7=-2-11x\)
- \(6x-14=8+x\)
- \(-x+15=1+6x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 15x \color{red}{-12}& = & 12 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12+14x }
& = & 12 \color{red}{ -14x }\color{blue}{+12+14x } \\\Leftrightarrow & 15x \color{blue}{+14x }
& = & 12 \color{blue}{+12} \\\Leftrightarrow &29x
& = &24\\\Leftrightarrow & \color{red}{29}x
& = &24\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}}
& = & \frac{24}{29} \\\Leftrightarrow & \color{green}{ x = \frac{24}{29} } & & \\ & V = \left\{ \frac{24}{29} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+3}& = & 2 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3+14x }
& = & 2 \color{red}{ -14x }\color{blue}{-3+14x } \\\Leftrightarrow & 5x \color{blue}{+14x }
& = & 2 \color{blue}{-3} \\\Leftrightarrow &19x
& = &-1\\\Leftrightarrow & \color{red}{19}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-8}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-3x }
& = & -3 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & -5x \color{blue}{-3x }
& = & -3 \color{blue}{+8} \\\Leftrightarrow &-8x
& = &5\\\Leftrightarrow & \color{red}{-8}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+11}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-x }
& = & 4 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 4 \color{blue}{-11} \\\Leftrightarrow &-6x
& = &-7\\\Leftrightarrow & \color{red}{-6}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+13}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13-13x }
& = & 13 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -3x \color{blue}{-13x }
& = & 13 \color{blue}{-13} \\\Leftrightarrow &-16x
& = &0\\\Leftrightarrow & \color{red}{-16}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-13}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-9x }
& = & -14 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -8x \color{blue}{-9x }
& = & -14 \color{blue}{+13} \\\Leftrightarrow &-17x
& = &-1\\\Leftrightarrow & \color{red}{-17}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-5}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-x }
& = & -5 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -5 \color{blue}{+5} \\\Leftrightarrow &-7x
& = &0\\\Leftrightarrow & \color{red}{-7}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-8}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8+2x }
& = & 2 \color{red}{ -2x }\color{blue}{+8+2x } \\\Leftrightarrow & 3x \color{blue}{+2x }
& = & 2 \color{blue}{+8} \\\Leftrightarrow &5x
& = &10\\\Leftrightarrow & \color{red}{5}x
& = &10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{10}{5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+2}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2-7x }
& = & 10 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & 10x \color{blue}{-7x }
& = & 10 \color{blue}{-2} \\\Leftrightarrow &3x
& = &8\\\Leftrightarrow & \color{red}{3}x
& = &8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+7}& = & -2 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7+11x }
& = & -2 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 14x \color{blue}{+11x }
& = & -2 \color{blue}{-7} \\\Leftrightarrow &25x
& = &-9\\\Leftrightarrow & \color{red}{25}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{-9}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{25} } & & \\ & V = \left\{ \frac{-9}{25} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-14}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14-x }
& = & 8 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & 8 \color{blue}{+14} \\\Leftrightarrow &5x
& = &22\\\Leftrightarrow & \color{red}{5}x
& = &22\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{22}{5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+15}& = & 1 \color{red}{ +6x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15-6x }
& = & 1 \color{red}{ +6x }\color{blue}{-15-6x } \\\Leftrightarrow & -x \color{blue}{-6x }
& = & 1 \color{blue}{-15} \\\Leftrightarrow &-7x
& = &-14\\\Leftrightarrow & \color{red}{-7}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-14}{-7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)