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