Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-13x-15=-4+x\)
- \(-14x-8=15+x\)
- \(11x-12=9+14x\)
- \(-7x+1=-15+x\)
- \(13x+13=-10-6x\)
- \(-x-6=7+2x\)
- \(-6x+8=-14+7x\)
- \(4x-1=15+x\)
- \(-8x+10=-11+x\)
- \(7x-11=11-6x\)
- \(2x-9=9+7x\)
- \(-12x-3=-12+13x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -13x \color{red}{-15}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-x }
& = & -4 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -4 \color{blue}{+15} \\\Leftrightarrow &-14x
& = &11\\\Leftrightarrow & \color{red}{-14}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-8}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x }
& = & 15 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 15 \color{blue}{+8} \\\Leftrightarrow &-15x
& = &23\\\Leftrightarrow & \color{red}{-15}x
& = &23\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{23}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{15} } & & \\ & V = \left\{ \frac{-23}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-12}& = & 9 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12-14x }
& = & 9 \color{red}{ +14x }\color{blue}{+12-14x } \\\Leftrightarrow & 11x \color{blue}{-14x }
& = & 9 \color{blue}{+12} \\\Leftrightarrow &-3x
& = &21\\\Leftrightarrow & \color{red}{-3}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{21}{-3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x }
& = & -15 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -15 \color{blue}{-1} \\\Leftrightarrow &-8x
& = &-16\\\Leftrightarrow & \color{red}{-8}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-16}{-8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+13}& = & -10 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13+6x }
& = & -10 \color{red}{ -6x }\color{blue}{-13+6x } \\\Leftrightarrow & 13x \color{blue}{+6x }
& = & -10 \color{blue}{-13} \\\Leftrightarrow &19x
& = &-23\\\Leftrightarrow & \color{red}{19}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-23}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{19} } & & \\ & V = \left\{ \frac{-23}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-6}& = & 7 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6-2x }
& = & 7 \color{red}{ +2x }\color{blue}{+6-2x } \\\Leftrightarrow & -x \color{blue}{-2x }
& = & 7 \color{blue}{+6} \\\Leftrightarrow &-3x
& = &13\\\Leftrightarrow & \color{red}{-3}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+8}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-7x }
& = & -14 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & -14 \color{blue}{-8} \\\Leftrightarrow &-13x
& = &-22\\\Leftrightarrow & \color{red}{-13}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-1}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1-x }
& = & 15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 4x \color{blue}{-x }
& = & 15 \color{blue}{+1} \\\Leftrightarrow &3x
& = &16\\\Leftrightarrow & \color{red}{3}x
& = &16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+10}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+10}\color{blue}{-10-x }
& = & -11 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & -11 \color{blue}{-10} \\\Leftrightarrow &-9x
& = &-21\\\Leftrightarrow & \color{red}{-9}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-11}& = & 11 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11+6x }
& = & 11 \color{red}{ -6x }\color{blue}{+11+6x } \\\Leftrightarrow & 7x \color{blue}{+6x }
& = & 11 \color{blue}{+11} \\\Leftrightarrow &13x
& = &22\\\Leftrightarrow & \color{red}{13}x
& = &22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-9}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-9}\color{blue}{+9-7x }
& = & 9 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & 2x \color{blue}{-7x }
& = & 9 \color{blue}{+9} \\\Leftrightarrow &-5x
& = &18\\\Leftrightarrow & \color{red}{-5}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-3}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-13x }
& = & -12 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & -12 \color{blue}{+3} \\\Leftrightarrow &-25x
& = &-9\\\Leftrightarrow & \color{red}{-25}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-9}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{9}{25} } & & \\ & V = \left\{ \frac{9}{25} \right\} & \\\end{align}\)