Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(3x-12=2-11x\)
- \(8x+5=-3-7x\)
- \(7x-4=5-9x\)
- \(15x+4=-2+13x\)
- \(-15x+10=-2+13x\)
- \(-6x-15=-1+7x\)
- \(12x+6=5-7x\)
- \(-7x+4=-3+11x\)
- \(x+6=-7-15x\)
- \(12x-15=-9+x\)
- \(-14x+13=9+x\)
- \(x-7=-8-2x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 3x \color{red}{-12}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+11x }
& = & 2 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 3x \color{blue}{+11x }
& = & 2 \color{blue}{+12} \\\Leftrightarrow &14x
& = &14\\\Leftrightarrow & \color{red}{14}x
& = &14\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{14}{14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+5}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5+7x }
& = & -3 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & 8x \color{blue}{+7x }
& = & -3 \color{blue}{-5} \\\Leftrightarrow &15x
& = &-8\\\Leftrightarrow & \color{red}{15}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{-8}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-4}& = & 5 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4+9x }
& = & 5 \color{red}{ -9x }\color{blue}{+4+9x } \\\Leftrightarrow & 7x \color{blue}{+9x }
& = & 5 \color{blue}{+4} \\\Leftrightarrow &16x
& = &9\\\Leftrightarrow & \color{red}{16}x
& = &9\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}}
& = & \frac{9}{16} \\\Leftrightarrow & \color{green}{ x = \frac{9}{16} } & & \\ & V = \left\{ \frac{9}{16} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+4}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4-13x }
& = & -2 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & 15x \color{blue}{-13x }
& = & -2 \color{blue}{-4} \\\Leftrightarrow &2x
& = &-6\\\Leftrightarrow & \color{red}{2}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{-6}{2} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+10}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-13x }
& = & -2 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & -2 \color{blue}{-10} \\\Leftrightarrow &-28x
& = &-12\\\Leftrightarrow & \color{red}{-28}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{-12}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-15}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-7x }
& = & -1 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & -1 \color{blue}{+15} \\\Leftrightarrow &-13x
& = &14\\\Leftrightarrow & \color{red}{-13}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+6}& = & 5 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6+7x }
& = & 5 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 12x \color{blue}{+7x }
& = & 5 \color{blue}{-6} \\\Leftrightarrow &19x
& = &-1\\\Leftrightarrow & \color{red}{19}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+4}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-11x }
& = & -3 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & -7x \color{blue}{-11x }
& = & -3 \color{blue}{-4} \\\Leftrightarrow &-18x
& = &-7\\\Leftrightarrow & \color{red}{-18}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}}
& = & \frac{-7}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{7}{18} } & & \\ & V = \left\{ \frac{7}{18} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+6}& = & -7 \color{red}{ -15x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6+15x }
& = & -7 \color{red}{ -15x }\color{blue}{-6+15x } \\\Leftrightarrow & x \color{blue}{+15x }
& = & -7 \color{blue}{-6} \\\Leftrightarrow &16x
& = &-13\\\Leftrightarrow & \color{red}{16}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}}
& = & \frac{-13}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{16} } & & \\ & V = \left\{ \frac{-13}{16} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-15}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15-x }
& = & -9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & -9 \color{blue}{+15} \\\Leftrightarrow &11x
& = &6\\\Leftrightarrow & \color{red}{11}x
& = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+13}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x }
& = & 9 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 9 \color{blue}{-13} \\\Leftrightarrow &-15x
& = &-4\\\Leftrightarrow & \color{red}{-15}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-7}& = & -8 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7+2x }
& = & -8 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & x \color{blue}{+2x }
& = & -8 \color{blue}{+7} \\\Leftrightarrow &3x
& = &-1\\\Leftrightarrow & \color{red}{3}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{-1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)