Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(10x+3=13+7x\)
- \(6x+12=-12+x\)
- \(-5x+5=1+3x\)
- \(-6x-6=3+x\)
- \(12x+1=13+7x\)
- \(4x+6=-10-7x\)
- \(-15x+12=12+13x\)
- \(3x-8=-9-8x\)
- \(10x-9=-10+3x\)
- \(-12x-1=-14+13x\)
- \(-12x+14=6+5x\)
- \(6x+15=-14+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 10x \color{red}{+3}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3-7x }
& = & 13 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & 10x \color{blue}{-7x }
& = & 13 \color{blue}{-3} \\\Leftrightarrow &3x
& = &10\\\Leftrightarrow & \color{red}{3}x
& = &10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+12}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12-x }
& = & -12 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & -12 \color{blue}{-12} \\\Leftrightarrow &5x
& = &-24\\\Leftrightarrow & \color{red}{5}x
& = &-24\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-24}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{5} } & & \\ & V = \left\{ \frac{-24}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+5}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-3x }
& = & 1 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & -5x \color{blue}{-3x }
& = & 1 \color{blue}{-5} \\\Leftrightarrow &-8x
& = &-4\\\Leftrightarrow & \color{red}{-8}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-x }
& = & 3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & 3 \color{blue}{+6} \\\Leftrightarrow &-7x
& = &9\\\Leftrightarrow & \color{red}{-7}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+1}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1-7x }
& = & 13 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 12x \color{blue}{-7x }
& = & 13 \color{blue}{-1} \\\Leftrightarrow &5x
& = &12\\\Leftrightarrow & \color{red}{5}x
& = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+6}& = & -10 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6+7x }
& = & -10 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 4x \color{blue}{+7x }
& = & -10 \color{blue}{-6} \\\Leftrightarrow &11x
& = &-16\\\Leftrightarrow & \color{red}{11}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+12}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-13x }
& = & 12 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & 12 \color{blue}{-12} \\\Leftrightarrow &-28x
& = &0\\\Leftrightarrow & \color{red}{-28}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{0}{-28} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-8}& = & -9 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8+8x }
& = & -9 \color{red}{ -8x }\color{blue}{+8+8x } \\\Leftrightarrow & 3x \color{blue}{+8x }
& = & -9 \color{blue}{+8} \\\Leftrightarrow &11x
& = &-1\\\Leftrightarrow & \color{red}{11}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-9}& = & -10 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9-3x }
& = & -10 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & 10x \color{blue}{-3x }
& = & -10 \color{blue}{+9} \\\Leftrightarrow &7x
& = &-1\\\Leftrightarrow & \color{red}{7}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{-1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-1}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-13x }
& = & -14 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & -14 \color{blue}{+1} \\\Leftrightarrow &-25x
& = &-13\\\Leftrightarrow & \color{red}{-25}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-13}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{13}{25} } & & \\ & V = \left\{ \frac{13}{25} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+14}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-5x }
& = & 6 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & -12x \color{blue}{-5x }
& = & 6 \color{blue}{-14} \\\Leftrightarrow &-17x
& = &-8\\\Leftrightarrow & \color{red}{-17}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15-x }
& = & -14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & -14 \color{blue}{-15} \\\Leftrightarrow &5x
& = &-29\\\Leftrightarrow & \color{red}{5}x
& = &-29\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-29}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{5} } & & \\ & V = \left\{ \frac{-29}{5} \right\} & \\\end{align}\)