Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-10x+15=14+x\)
- \(-7x+13=6+11x\)
- \(7x-2=-2+2x\)
- \(6x+13=-10+13x\)
- \(-2x+15=-9+11x\)
- \(5x+11=14+8x\)
- \(7x-5=-13-13x\)
- \(-9x+11=3+x\)
- \(-x-9=-15-10x\)
- \(-4x-7=-4+x\)
- \(3x+3=-4-8x\)
- \(-5x-10=5+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -10x \color{red}{+15}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15-x }
& = & 14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 14 \color{blue}{-15} \\\Leftrightarrow &-11x
& = &-1\\\Leftrightarrow & \color{red}{-11}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+13}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-11x }
& = & 6 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & -7x \color{blue}{-11x }
& = & 6 \color{blue}{-13} \\\Leftrightarrow &-18x
& = &-7\\\Leftrightarrow & \color{red}{-18}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}}
& = & \frac{-7}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{7}{18} } & & \\ & V = \left\{ \frac{7}{18} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-2}& = & -2 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2-2x }
& = & -2 \color{red}{ +2x }\color{blue}{+2-2x } \\\Leftrightarrow & 7x \color{blue}{-2x }
& = & -2 \color{blue}{+2} \\\Leftrightarrow &5x
& = &0\\\Leftrightarrow & \color{red}{5}x
& = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+13}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13-13x }
& = & -10 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & 6x \color{blue}{-13x }
& = & -10 \color{blue}{-13} \\\Leftrightarrow &-7x
& = &-23\\\Leftrightarrow & \color{red}{-7}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+15}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15-11x }
& = & -9 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & -2x \color{blue}{-11x }
& = & -9 \color{blue}{-15} \\\Leftrightarrow &-13x
& = &-24\\\Leftrightarrow & \color{red}{-13}x
& = &-24\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-24}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{24}{13} } & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+11}& = & 14 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11-8x }
& = & 14 \color{red}{ +8x }\color{blue}{-11-8x } \\\Leftrightarrow & 5x \color{blue}{-8x }
& = & 14 \color{blue}{-11} \\\Leftrightarrow &-3x
& = &3\\\Leftrightarrow & \color{red}{-3}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{3}{-3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-5}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5+13x }
& = & -13 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 7x \color{blue}{+13x }
& = & -13 \color{blue}{+5} \\\Leftrightarrow &20x
& = &-8\\\Leftrightarrow & \color{red}{20}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{-8}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-x }
& = & 3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 3 \color{blue}{-11} \\\Leftrightarrow &-10x
& = &-8\\\Leftrightarrow & \color{red}{-10}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-9}& = & -15 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9+10x }
& = & -15 \color{red}{ -10x }\color{blue}{+9+10x } \\\Leftrightarrow & -x \color{blue}{+10x }
& = & -15 \color{blue}{+9} \\\Leftrightarrow &9x
& = &-6\\\Leftrightarrow & \color{red}{9}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-7}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-x }
& = & -4 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -4 \color{blue}{+7} \\\Leftrightarrow &-5x
& = &3\\\Leftrightarrow & \color{red}{-5}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+3}& = & -4 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3+8x }
& = & -4 \color{red}{ -8x }\color{blue}{-3+8x } \\\Leftrightarrow & 3x \color{blue}{+8x }
& = & -4 \color{blue}{-3} \\\Leftrightarrow &11x
& = &-7\\\Leftrightarrow & \color{red}{11}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-10}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-x }
& = & 5 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 5 \color{blue}{+10} \\\Leftrightarrow &-6x
& = &15\\\Leftrightarrow & \color{red}{-6}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)