Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-3x-13=10+10x\)
- \(-4x+14=-1+x\)
- \(3x+14=-10+x\)
- \(5x-9=13+x\)
- \(15x-2=13+4x\)
- \(-8x+14=-14+9x\)
- \(13x-5=-11+9x\)
- \(15x+1=1+13x\)
- \(4x+13=1-11x\)
- \(-5x+6=4+x\)
- \(-6x+3=-14+x\)
- \(9x-14=10+10x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -3x \color{red}{-13}& = & 10 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-10x }
& = & 10 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & -3x \color{blue}{-10x }
& = & 10 \color{blue}{+13} \\\Leftrightarrow &-13x
& = &23\\\Leftrightarrow & \color{red}{-13}x
& = &23\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{23}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{13} } & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+14}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14-x }
& = & -1 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -1 \color{blue}{-14} \\\Leftrightarrow &-5x
& = &-15\\\Leftrightarrow & \color{red}{-5}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-15}{-5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+14}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14-x }
& = & -10 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 3x \color{blue}{-x }
& = & -10 \color{blue}{-14} \\\Leftrightarrow &2x
& = &-24\\\Leftrightarrow & \color{red}{2}x
& = &-24\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{-24}{2} \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9-x }
& = & 13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 5x \color{blue}{-x }
& = & 13 \color{blue}{+9} \\\Leftrightarrow &4x
& = &22\\\Leftrightarrow & \color{red}{4}x
& = &22\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{22}{4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-2}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2-4x }
& = & 13 \color{red}{ +4x }\color{blue}{+2-4x } \\\Leftrightarrow & 15x \color{blue}{-4x }
& = & 13 \color{blue}{+2} \\\Leftrightarrow &11x
& = &15\\\Leftrightarrow & \color{red}{11}x
& = &15\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{15}{11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+14}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-9x }
& = & -14 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & -8x \color{blue}{-9x }
& = & -14 \color{blue}{-14} \\\Leftrightarrow &-17x
& = &-28\\\Leftrightarrow & \color{red}{-17}x
& = &-28\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-28}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{28}{17} } & & \\ & V = \left\{ \frac{28}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-5}& = & -11 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5-9x }
& = & -11 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & 13x \color{blue}{-9x }
& = & -11 \color{blue}{+5} \\\Leftrightarrow &4x
& = &-6\\\Leftrightarrow & \color{red}{4}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{-6}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+1}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1-13x }
& = & 1 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & 15x \color{blue}{-13x }
& = & 1 \color{blue}{-1} \\\Leftrightarrow &2x
& = &0\\\Leftrightarrow & \color{red}{2}x
& = &0\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{0}{2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+13}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13+11x }
& = & 1 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 4x \color{blue}{+11x }
& = & 1 \color{blue}{-13} \\\Leftrightarrow &15x
& = &-12\\\Leftrightarrow & \color{red}{15}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{-12}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+6}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-x }
& = & 4 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 4 \color{blue}{-6} \\\Leftrightarrow &-6x
& = &-2\\\Leftrightarrow & \color{red}{-6}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+3}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-x }
& = & -14 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -14 \color{blue}{-3} \\\Leftrightarrow &-7x
& = &-17\\\Leftrightarrow & \color{red}{-7}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-14}& = & 10 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14-10x }
& = & 10 \color{red}{ +10x }\color{blue}{+14-10x } \\\Leftrightarrow & 9x \color{blue}{-10x }
& = & 10 \color{blue}{+14} \\\Leftrightarrow &-x
& = &24\\\Leftrightarrow & \color{red}{-}x
& = &24\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{24}{-1} \\\Leftrightarrow & \color{green}{ x = -24 } & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)