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