Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-5x-11=3+x\)
- \(-2x+14=-7+13x\)
- \(4x-8=14+11x\)
- \(14x+10=-1+9x\)
- \(-3x+10=-13+x\)
- \(2x-6=10+7x\)
- \(-3x-6=-6+x\)
- \(11x-12=10-5x\)
- \(10x-13=-14+x\)
- \(-7x-12=-6+x\)
- \(7x+8=13-3x\)
- \(-7x-6=-9+8x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -5x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-x }
& = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 3 \color{blue}{+11} \\\Leftrightarrow &-6x
& = &14\\\Leftrightarrow & \color{red}{-6}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+14}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-13x }
& = & -7 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -2x \color{blue}{-13x }
& = & -7 \color{blue}{-14} \\\Leftrightarrow &-15x
& = &-21\\\Leftrightarrow & \color{red}{-15}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-21}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-8}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8-11x }
& = & 14 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & 4x \color{blue}{-11x }
& = & 14 \color{blue}{+8} \\\Leftrightarrow &-7x
& = &22\\\Leftrightarrow & \color{red}{-7}x
& = &22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+10}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10-9x }
& = & -1 \color{red}{ +9x }\color{blue}{-10-9x } \\\Leftrightarrow & 14x \color{blue}{-9x }
& = & -1 \color{blue}{-10} \\\Leftrightarrow &5x
& = &-11\\\Leftrightarrow & \color{red}{5}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-x }
& = & -13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -13 \color{blue}{-10} \\\Leftrightarrow &-4x
& = &-23\\\Leftrightarrow & \color{red}{-4}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-23}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{23}{4} } & & \\ & V = \left\{ \frac{23}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-6}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-7x }
& = & 10 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 2x \color{blue}{-7x }
& = & 10 \color{blue}{+6} \\\Leftrightarrow &-5x
& = &16\\\Leftrightarrow & \color{red}{-5}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-6}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x }
& = & -6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -6 \color{blue}{+6} \\\Leftrightarrow &-4x
& = &0\\\Leftrightarrow & \color{red}{-4}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-12}& = & 10 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12+5x }
& = & 10 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & 11x \color{blue}{+5x }
& = & 10 \color{blue}{+12} \\\Leftrightarrow &16x
& = &22\\\Leftrightarrow & \color{red}{16}x
& = &22\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}}
& = & \frac{22}{16} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13-x }
& = & -14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 10x \color{blue}{-x }
& = & -14 \color{blue}{+13} \\\Leftrightarrow &9x
& = &-1\\\Leftrightarrow & \color{red}{9}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-12}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-x }
& = & -6 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -6 \color{blue}{+12} \\\Leftrightarrow &-8x
& = &6\\\Leftrightarrow & \color{red}{-8}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+8}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8+3x }
& = & 13 \color{red}{ -3x }\color{blue}{-8+3x } \\\Leftrightarrow & 7x \color{blue}{+3x }
& = & 13 \color{blue}{-8} \\\Leftrightarrow &10x
& = &5\\\Leftrightarrow & \color{red}{10}x
& = &5\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{5}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-6}& = & -9 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-8x }
& = & -9 \color{red}{ +8x }\color{blue}{+6-8x } \\\Leftrightarrow & -7x \color{blue}{-8x }
& = & -9 \color{blue}{+6} \\\Leftrightarrow &-15x
& = &-3\\\Leftrightarrow & \color{red}{-15}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)