Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(13x+1=-1-6x\)
- \(-15x-6=-7+x\)
- \(-14x-13=1+x\)
- \(x-12=3-10x\)
- \(-6x+13=-4+x\)
- \(-10x+9=-13+x\)
- \(-11x+13=-1+x\)
- \(-13x+10=-9+8x\)
- \(-13x+3=-9+x\)
- \(7x+10=-13-2x\)
- \(-6x-5=-1+7x\)
- \(11x+14=12+13x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 13x \color{red}{+1}& = & -1 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1+6x }
& = & -1 \color{red}{ -6x }\color{blue}{-1+6x } \\\Leftrightarrow & 13x \color{blue}{+6x }
& = & -1 \color{blue}{-1} \\\Leftrightarrow &19x
& = &-2\\\Leftrightarrow & \color{red}{19}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-x }
& = & -7 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & -7 \color{blue}{+6} \\\Leftrightarrow &-16x
& = &-1\\\Leftrightarrow & \color{red}{-16}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-13}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13-x }
& = & 1 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 1 \color{blue}{+13} \\\Leftrightarrow &-15x
& = &14\\\Leftrightarrow & \color{red}{-15}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-12}& = & 3 \color{red}{ -10x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12+10x }
& = & 3 \color{red}{ -10x }\color{blue}{+12+10x } \\\Leftrightarrow & x \color{blue}{+10x }
& = & 3 \color{blue}{+12} \\\Leftrightarrow &11x
& = &15\\\Leftrightarrow & \color{red}{11}x
& = &15\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{15}{11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+13}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-x }
& = & -4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -4 \color{blue}{-13} \\\Leftrightarrow &-7x
& = &-17\\\Leftrightarrow & \color{red}{-7}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-x }
& = & -13 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -13 \color{blue}{-9} \\\Leftrightarrow &-11x
& = &-22\\\Leftrightarrow & \color{red}{-11}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-22}{-11} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13-x }
& = & -1 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -1 \color{blue}{-13} \\\Leftrightarrow &-12x
& = &-14\\\Leftrightarrow & \color{red}{-12}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+10}& = & -9 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{+10}\color{blue}{-10-8x }
& = & -9 \color{red}{ +8x }\color{blue}{-10-8x } \\\Leftrightarrow & -13x \color{blue}{-8x }
& = & -9 \color{blue}{-10} \\\Leftrightarrow &-21x
& = &-19\\\Leftrightarrow & \color{red}{-21}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}}
& = & \frac{-19}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{19}{21} } & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+3}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-x }
& = & -9 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -9 \color{blue}{-3} \\\Leftrightarrow &-14x
& = &-12\\\Leftrightarrow & \color{red}{-14}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+10}& = & -13 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10+2x }
& = & -13 \color{red}{ -2x }\color{blue}{-10+2x } \\\Leftrightarrow & 7x \color{blue}{+2x }
& = & -13 \color{blue}{-10} \\\Leftrightarrow &9x
& = &-23\\\Leftrightarrow & \color{red}{9}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-23}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{9} } & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-5}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-7x }
& = & -1 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & -1 \color{blue}{+5} \\\Leftrightarrow &-13x
& = &4\\\Leftrightarrow & \color{red}{-13}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+14}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14-13x }
& = & 12 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & 11x \color{blue}{-13x }
& = & 12 \color{blue}{-14} \\\Leftrightarrow &-2x
& = &-2\\\Leftrightarrow & \color{red}{-2}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}}
& = & \frac{-2}{-2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)