Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(5x+12=9-9x\)
- \(-11x+3=-2+x\)
- \(-2x+6=-2+x\)
- \(-6x+13=-4+x\)
- \(-15x+3=-4+x\)
- \(-8x-9=-10+x\)
- \(12x+2=2+x\)
- \(-10x-6=15+7x\)
- \(-8x+15=12+x\)
- \(-10x-8=-12+x\)
- \(11x-11=15-7x\)
- \(3x+14=-6+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 5x \color{red}{+12}& = & 9 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12+9x }
& = & 9 \color{red}{ -9x }\color{blue}{-12+9x } \\\Leftrightarrow & 5x \color{blue}{+9x }
& = & 9 \color{blue}{-12} \\\Leftrightarrow &14x
& = &-3\\\Leftrightarrow & \color{red}{14}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{-3}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+3}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-x }
& = & -2 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -2 \color{blue}{-3} \\\Leftrightarrow &-12x
& = &-5\\\Leftrightarrow & \color{red}{-12}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+6}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-x }
& = & -2 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & -2 \color{blue}{-6} \\\Leftrightarrow &-3x
& = &-8\\\Leftrightarrow & \color{red}{-3}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+13}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-x }
& = & -4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -4 \color{blue}{-13} \\\Leftrightarrow &-7x
& = &-17\\\Leftrightarrow & \color{red}{-7}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+3}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+3}\color{blue}{-3-x }
& = & -4 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & -4 \color{blue}{-3} \\\Leftrightarrow &-16x
& = &-7\\\Leftrightarrow & \color{red}{-16}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9-x }
& = & -10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & -10 \color{blue}{+9} \\\Leftrightarrow &-9x
& = &-1\\\Leftrightarrow & \color{red}{-9}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+2}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2-x }
& = & 2 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & 2 \color{blue}{-2} \\\Leftrightarrow &11x
& = &0\\\Leftrightarrow & \color{red}{11}x
& = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-6}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6-7x }
& = & 15 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -10x \color{blue}{-7x }
& = & 15 \color{blue}{+6} \\\Leftrightarrow &-17x
& = &21\\\Leftrightarrow & \color{red}{-17}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{21}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{17} } & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-x }
& = & 12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 12 \color{blue}{-15} \\\Leftrightarrow &-9x
& = &-3\\\Leftrightarrow & \color{red}{-9}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-8}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-8}\color{blue}{+8-x }
& = & -12 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -12 \color{blue}{+8} \\\Leftrightarrow &-11x
& = &-4\\\Leftrightarrow & \color{red}{-11}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-11}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11+7x }
& = & 15 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & 11x \color{blue}{+7x }
& = & 15 \color{blue}{+11} \\\Leftrightarrow &18x
& = &26\\\Leftrightarrow & \color{red}{18}x
& = &26\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}}
& = & \frac{26}{18} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14-x }
& = & -6 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 3x \color{blue}{-x }
& = & -6 \color{blue}{-14} \\\Leftrightarrow &2x
& = &-20\\\Leftrightarrow & \color{red}{2}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{-20}{2} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)