Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(4x-4=14-7x\)
- \(-14x-11=3+5x\)
- \(13x-12=10+10x\)
- \(3x-11=7+7x\)
- \(-6x+15=-11+x\)
- \(-x+5=11+13x\)
- \(-12x+10=-6+13x\)
- \(3x-7=8+4x\)
- \(-11x-6=13+x\)
- \(x+6=-6+6x\)
- \(10x+3=12-9x\)
- \(-3x-12=-13+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 4x \color{red}{-4}& = & 14 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4+7x }
& = & 14 \color{red}{ -7x }\color{blue}{+4+7x } \\\Leftrightarrow & 4x \color{blue}{+7x }
& = & 14 \color{blue}{+4} \\\Leftrightarrow &11x
& = &18\\\Leftrightarrow & \color{red}{11}x
& = &18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-11}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-5x }
& = & 3 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & -14x \color{blue}{-5x }
& = & 3 \color{blue}{+11} \\\Leftrightarrow &-19x
& = &14\\\Leftrightarrow & \color{red}{-19}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{14}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{19} } & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-12}& = & 10 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12-10x }
& = & 10 \color{red}{ +10x }\color{blue}{+12-10x } \\\Leftrightarrow & 13x \color{blue}{-10x }
& = & 10 \color{blue}{+12} \\\Leftrightarrow &3x
& = &22\\\Leftrightarrow & \color{red}{3}x
& = &22\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{22}{3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-11}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11-7x }
& = & 7 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & 3x \color{blue}{-7x }
& = & 7 \color{blue}{+11} \\\Leftrightarrow &-4x
& = &18\\\Leftrightarrow & \color{red}{-4}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{18}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15-x }
& = & -11 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -11 \color{blue}{-15} \\\Leftrightarrow &-7x
& = &-26\\\Leftrightarrow & \color{red}{-7}x
& = &-26\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-26}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{26}{7} } & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+5}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5-13x }
& = & 11 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -x \color{blue}{-13x }
& = & 11 \color{blue}{-5} \\\Leftrightarrow &-14x
& = &6\\\Leftrightarrow & \color{red}{-14}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+10}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10-13x }
& = & -6 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & -6 \color{blue}{-10} \\\Leftrightarrow &-25x
& = &-16\\\Leftrightarrow & \color{red}{-25}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-16}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{16}{25} } & & \\ & V = \left\{ \frac{16}{25} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-7}& = & 8 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7-4x }
& = & 8 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & 3x \color{blue}{-4x }
& = & 8 \color{blue}{+7} \\\Leftrightarrow &-x
& = &15\\\Leftrightarrow & \color{red}{-}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{15}{-1} \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-x }
& = & 13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 13 \color{blue}{+6} \\\Leftrightarrow &-12x
& = &19\\\Leftrightarrow & \color{red}{-12}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{19}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{12} } & & \\ & V = \left\{ \frac{-19}{12} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+6}& = & -6 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6-6x }
& = & -6 \color{red}{ +6x }\color{blue}{-6-6x } \\\Leftrightarrow & x \color{blue}{-6x }
& = & -6 \color{blue}{-6} \\\Leftrightarrow &-5x
& = &-12\\\Leftrightarrow & \color{red}{-5}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+3}& = & 12 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3+9x }
& = & 12 \color{red}{ -9x }\color{blue}{-3+9x } \\\Leftrightarrow & 10x \color{blue}{+9x }
& = & 12 \color{blue}{-3} \\\Leftrightarrow &19x
& = &9\\\Leftrightarrow & \color{red}{19}x
& = &9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{9}{19} } & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-12}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12-x }
& = & -13 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -13 \color{blue}{+12} \\\Leftrightarrow &-4x
& = &-1\\\Leftrightarrow & \color{red}{-4}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)