Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(9x-3=-11-13x\)
- \(8x+7=-10-13x\)
- \(-12x+2=-12+x\)
- \(-14x+1=15+x\)
- \(9x+3=-2+4x\)
- \(3x+4=4-8x\)
- \(9x-8=6-8x\)
- \(-8x-2=-12+x\)
- \(5x+7=2-2x\)
- \(-x-3=2+2x\)
- \(7x-9=11+10x\)
- \(-15x-15=-1+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 9x \color{red}{-3}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3+13x }
& = & -11 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 9x \color{blue}{+13x }
& = & -11 \color{blue}{+3} \\\Leftrightarrow &22x
& = &-8\\\Leftrightarrow & \color{red}{22}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}}
& = & \frac{-8}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+7}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7+13x }
& = & -10 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 8x \color{blue}{+13x }
& = & -10 \color{blue}{-7} \\\Leftrightarrow &21x
& = &-17\\\Leftrightarrow & \color{red}{21}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}}
& = & \frac{-17}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{21} } & & \\ & V = \left\{ \frac{-17}{21} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+2}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-x }
& = & -12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -12 \color{blue}{-2} \\\Leftrightarrow &-13x
& = &-14\\\Leftrightarrow & \color{red}{-13}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+1}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x }
& = & 15 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 15 \color{blue}{-1} \\\Leftrightarrow &-15x
& = &14\\\Leftrightarrow & \color{red}{-15}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+3}& = & -2 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3-4x }
& = & -2 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & 9x \color{blue}{-4x }
& = & -2 \color{blue}{-3} \\\Leftrightarrow &5x
& = &-5\\\Leftrightarrow & \color{red}{5}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+4}& = & 4 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4+8x }
& = & 4 \color{red}{ -8x }\color{blue}{-4+8x } \\\Leftrightarrow & 3x \color{blue}{+8x }
& = & 4 \color{blue}{-4} \\\Leftrightarrow &11x
& = &0\\\Leftrightarrow & \color{red}{11}x
& = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-8}& = & 6 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8+8x }
& = & 6 \color{red}{ -8x }\color{blue}{+8+8x } \\\Leftrightarrow & 9x \color{blue}{+8x }
& = & 6 \color{blue}{+8} \\\Leftrightarrow &17x
& = &14\\\Leftrightarrow & \color{red}{17}x
& = &14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-2}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2-x }
& = & -12 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & -12 \color{blue}{+2} \\\Leftrightarrow &-9x
& = &-10\\\Leftrightarrow & \color{red}{-9}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+7}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7+2x }
& = & 2 \color{red}{ -2x }\color{blue}{-7+2x } \\\Leftrightarrow & 5x \color{blue}{+2x }
& = & 2 \color{blue}{-7} \\\Leftrightarrow &7x
& = &-5\\\Leftrightarrow & \color{red}{7}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-3}& = & 2 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3-2x }
& = & 2 \color{red}{ +2x }\color{blue}{+3-2x } \\\Leftrightarrow & -x \color{blue}{-2x }
& = & 2 \color{blue}{+3} \\\Leftrightarrow &-3x
& = &5\\\Leftrightarrow & \color{red}{-3}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-9}& = & 11 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9-10x }
& = & 11 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & 7x \color{blue}{-10x }
& = & 11 \color{blue}{+9} \\\Leftrightarrow &-3x
& = &20\\\Leftrightarrow & \color{red}{-3}x
& = &20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-15}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-x }
& = & -1 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & -1 \color{blue}{+15} \\\Leftrightarrow &-16x
& = &14\\\Leftrightarrow & \color{red}{-16}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)