Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-3x+15=-7+4x\)
- \(9x+3=15-8x\)
- \(4x-2=3+9x\)
- \(-4x-11=2+5x\)
- \(-x-11=-2-7x\)
- \(-10x+15=4+x\)
- \(7x+12=-6-3x\)
- \(4x-8=9+x\)
- \(12x-3=7-11x\)
- \(-11x-6=-6+x\)
- \(10x-1=10+13x\)
- \(-9x-11=3+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -3x \color{red}{+15}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-4x }
& = & -7 \color{red}{ +4x }\color{blue}{-15-4x } \\\Leftrightarrow & -3x \color{blue}{-4x }
& = & -7 \color{blue}{-15} \\\Leftrightarrow &-7x
& = &-22\\\Leftrightarrow & \color{red}{-7}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{22}{7} } & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+3}& = & 15 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3+8x }
& = & 15 \color{red}{ -8x }\color{blue}{-3+8x } \\\Leftrightarrow & 9x \color{blue}{+8x }
& = & 15 \color{blue}{-3} \\\Leftrightarrow &17x
& = &12\\\Leftrightarrow & \color{red}{17}x
& = &12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-2}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2-9x }
& = & 3 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & 4x \color{blue}{-9x }
& = & 3 \color{blue}{+2} \\\Leftrightarrow &-5x
& = &5\\\Leftrightarrow & \color{red}{-5}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-11}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-5x }
& = & 2 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & -4x \color{blue}{-5x }
& = & 2 \color{blue}{+11} \\\Leftrightarrow &-9x
& = &13\\\Leftrightarrow & \color{red}{-9}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-11}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11+7x }
& = & -2 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & -x \color{blue}{+7x }
& = & -2 \color{blue}{+11} \\\Leftrightarrow &6x
& = &9\\\Leftrightarrow & \color{red}{6}x
& = &9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}}
& = & \frac{9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+15}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15-x }
& = & 4 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 4 \color{blue}{-15} \\\Leftrightarrow &-11x
& = &-11\\\Leftrightarrow & \color{red}{-11}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+12}& = & -6 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12+3x }
& = & -6 \color{red}{ -3x }\color{blue}{-12+3x } \\\Leftrightarrow & 7x \color{blue}{+3x }
& = & -6 \color{blue}{-12} \\\Leftrightarrow &10x
& = &-18\\\Leftrightarrow & \color{red}{10}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{-18}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-8}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8-x }
& = & 9 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 4x \color{blue}{-x }
& = & 9 \color{blue}{+8} \\\Leftrightarrow &3x
& = &17\\\Leftrightarrow & \color{red}{3}x
& = &17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-3}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3+11x }
& = & 7 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & 7 \color{blue}{+3} \\\Leftrightarrow &23x
& = &10\\\Leftrightarrow & \color{red}{23}x
& = &10\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{10}{23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-6}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-x }
& = & -6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -6 \color{blue}{+6} \\\Leftrightarrow &-12x
& = &0\\\Leftrightarrow & \color{red}{-12}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-1}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-1}\color{blue}{+1-13x }
& = & 10 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 10x \color{blue}{-13x }
& = & 10 \color{blue}{+1} \\\Leftrightarrow &-3x
& = &11\\\Leftrightarrow & \color{red}{-3}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-x }
& = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 3 \color{blue}{+11} \\\Leftrightarrow &-10x
& = &14\\\Leftrightarrow & \color{red}{-10}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)