Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-14x-8=-5+x\)
- \(-11x+15=-11+14x\)
- \(-14x-10=-13+x\)
- \(-10x-9=-13+x\)
- \(15x-14=-13+2x\)
- \(-10x+14=-15+x\)
- \(-11x-13=-3+x\)
- \(3x+9=15+13x\)
- \(15x-14=9-7x\)
- \(13x-12=-3+5x\)
- \(-5x+9=-11+11x\)
- \(-4x-2=-12+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -14x \color{red}{-8}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x }
& = & -5 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -5 \color{blue}{+8} \\\Leftrightarrow &-15x
& = &3\\\Leftrightarrow & \color{red}{-15}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+15}& = & -11 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-14x }
& = & -11 \color{red}{ +14x }\color{blue}{-15-14x } \\\Leftrightarrow & -11x \color{blue}{-14x }
& = & -11 \color{blue}{-15} \\\Leftrightarrow &-25x
& = &-26\\\Leftrightarrow & \color{red}{-25}x
& = &-26\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-26}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{26}{25} } & & \\ & V = \left\{ \frac{26}{25} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10-x }
& = & -13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -13 \color{blue}{+10} \\\Leftrightarrow &-15x
& = &-3\\\Leftrightarrow & \color{red}{-15}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-x }
& = & -13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -13 \color{blue}{+9} \\\Leftrightarrow &-11x
& = &-4\\\Leftrightarrow & \color{red}{-11}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-14}& = & -13 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14-2x }
& = & -13 \color{red}{ +2x }\color{blue}{+14-2x } \\\Leftrightarrow & 15x \color{blue}{-2x }
& = & -13 \color{blue}{+14} \\\Leftrightarrow &13x
& = &1\\\Leftrightarrow & \color{red}{13}x
& = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+14}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x }
& = & -15 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -15 \color{blue}{-14} \\\Leftrightarrow &-11x
& = &-29\\\Leftrightarrow & \color{red}{-11}x
& = &-29\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-29}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{29}{11} } & & \\ & V = \left\{ \frac{29}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-13}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-x }
& = & -3 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -3 \color{blue}{+13} \\\Leftrightarrow &-12x
& = &10\\\Leftrightarrow & \color{red}{-12}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+9}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9-13x }
& = & 15 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & 3x \color{blue}{-13x }
& = & 15 \color{blue}{-9} \\\Leftrightarrow &-10x
& = &6\\\Leftrightarrow & \color{red}{-10}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-14}& = & 9 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14+7x }
& = & 9 \color{red}{ -7x }\color{blue}{+14+7x } \\\Leftrightarrow & 15x \color{blue}{+7x }
& = & 9 \color{blue}{+14} \\\Leftrightarrow &22x
& = &23\\\Leftrightarrow & \color{red}{22}x
& = &23\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}}
& = & \frac{23}{22} \\\Leftrightarrow & \color{green}{ x = \frac{23}{22} } & & \\ & V = \left\{ \frac{23}{22} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-12}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12-5x }
& = & -3 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & 13x \color{blue}{-5x }
& = & -3 \color{blue}{+12} \\\Leftrightarrow &8x
& = &9\\\Leftrightarrow & \color{red}{8}x
& = &9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+9}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9-11x }
& = & -11 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & -5x \color{blue}{-11x }
& = & -11 \color{blue}{-9} \\\Leftrightarrow &-16x
& = &-20\\\Leftrightarrow & \color{red}{-16}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-20}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-2}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2-x }
& = & -12 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -12 \color{blue}{+2} \\\Leftrightarrow &-5x
& = &-10\\\Leftrightarrow & \color{red}{-5}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)