Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-9x-15=-14+7x\)
- \(x+3=7+13x\)
- \(15x-3=14-7x\)
- \(15x+8=-1+4x\)
- \(3x-12=-7-8x\)
- \(-4x-14=-4+x\)
- \(-7x+14=-6+x\)
- \(-9x-12=-5+x\)
- \(4x+7=-5-11x\)
- \(-13x+9=-14+14x\)
- \(-6x-15=3+x\)
- \(-x-11=-14-10x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -9x \color{red}{-15}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-7x }
& = & -14 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -9x \color{blue}{-7x }
& = & -14 \color{blue}{+15} \\\Leftrightarrow &-16x
& = &1\\\Leftrightarrow & \color{red}{-16}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+3}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3-13x }
& = & 7 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & x \color{blue}{-13x }
& = & 7 \color{blue}{-3} \\\Leftrightarrow &-12x
& = &4\\\Leftrightarrow & \color{red}{-12}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-3}& = & 14 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-3}\color{blue}{+3+7x }
& = & 14 \color{red}{ -7x }\color{blue}{+3+7x } \\\Leftrightarrow & 15x \color{blue}{+7x }
& = & 14 \color{blue}{+3} \\\Leftrightarrow &22x
& = &17\\\Leftrightarrow & \color{red}{22}x
& = &17\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}}
& = & \frac{17}{22} \\\Leftrightarrow & \color{green}{ x = \frac{17}{22} } & & \\ & V = \left\{ \frac{17}{22} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+8}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8-4x }
& = & -1 \color{red}{ +4x }\color{blue}{-8-4x } \\\Leftrightarrow & 15x \color{blue}{-4x }
& = & -1 \color{blue}{-8} \\\Leftrightarrow &11x
& = &-9\\\Leftrightarrow & \color{red}{11}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-12}& = & -7 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+8x }
& = & -7 \color{red}{ -8x }\color{blue}{+12+8x } \\\Leftrightarrow & 3x \color{blue}{+8x }
& = & -7 \color{blue}{+12} \\\Leftrightarrow &11x
& = &5\\\Leftrightarrow & \color{red}{11}x
& = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-14}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14-x }
& = & -4 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -4 \color{blue}{+14} \\\Leftrightarrow &-5x
& = &10\\\Leftrightarrow & \color{red}{-5}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x }
& = & -6 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -6 \color{blue}{-14} \\\Leftrightarrow &-8x
& = &-20\\\Leftrightarrow & \color{red}{-8}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-12}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-x }
& = & -5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -5 \color{blue}{+12} \\\Leftrightarrow &-10x
& = &7\\\Leftrightarrow & \color{red}{-10}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+7}& = & -5 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7+11x }
& = & -5 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 4x \color{blue}{+11x }
& = & -5 \color{blue}{-7} \\\Leftrightarrow &15x
& = &-12\\\Leftrightarrow & \color{red}{15}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{-12}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+9}& = & -14 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-14x }
& = & -14 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & -13x \color{blue}{-14x }
& = & -14 \color{blue}{-9} \\\Leftrightarrow &-27x
& = &-23\\\Leftrightarrow & \color{red}{-27}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}}
& = & \frac{-23}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{23}{27} } & & \\ & V = \left\{ \frac{23}{27} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-15}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-x }
& = & 3 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & 3 \color{blue}{+15} \\\Leftrightarrow &-7x
& = &18\\\Leftrightarrow & \color{red}{-7}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-11}& = & -14 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11+10x }
& = & -14 \color{red}{ -10x }\color{blue}{+11+10x } \\\Leftrightarrow & -x \color{blue}{+10x }
& = & -14 \color{blue}{+11} \\\Leftrightarrow &9x
& = &-3\\\Leftrightarrow & \color{red}{9}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)