Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-15x-12=1+13x\)
- \(15x-9=-6+13x\)
- \(2x+15=10+x\)
- \(-14x+1=-13+x\)
- \(4x-2=-11+x\)
- \(-5x-9=-13+11x\)
- \(14x-1=15+5x\)
- \(11x+9=-5-13x\)
- \(-4x-15=-6+x\)
- \(5x+12=-9-2x\)
- \(11x+9=-1+x\)
- \(x+9=-8+7x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -15x \color{red}{-12}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-13x }
& = & 1 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & 1 \color{blue}{+12} \\\Leftrightarrow &-28x
& = &13\\\Leftrightarrow & \color{red}{-28}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{13}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{28} } & & \\ & V = \left\{ \frac{-13}{28} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-9}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9-13x }
& = & -6 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 15x \color{blue}{-13x }
& = & -6 \color{blue}{+9} \\\Leftrightarrow &2x
& = &3\\\Leftrightarrow & \color{red}{2}x
& = &3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+15}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x }
& = & 10 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & 10 \color{blue}{-15} \\\Leftrightarrow &x
& = &-5\\\Leftrightarrow & \color{red}{}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+1}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x }
& = & -13 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -13 \color{blue}{-1} \\\Leftrightarrow &-15x
& = &-14\\\Leftrightarrow & \color{red}{-15}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2-x }
& = & -11 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 4x \color{blue}{-x }
& = & -11 \color{blue}{+2} \\\Leftrightarrow &3x
& = &-9\\\Leftrightarrow & \color{red}{3}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{-9}{3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-9}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-11x }
& = & -13 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & -5x \color{blue}{-11x }
& = & -13 \color{blue}{+9} \\\Leftrightarrow &-16x
& = &-4\\\Leftrightarrow & \color{red}{-16}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-1}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1-5x }
& = & 15 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & 14x \color{blue}{-5x }
& = & 15 \color{blue}{+1} \\\Leftrightarrow &9x
& = &16\\\Leftrightarrow & \color{red}{9}x
& = &16\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{16}{9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+9}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9+13x }
& = & -5 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 11x \color{blue}{+13x }
& = & -5 \color{blue}{-9} \\\Leftrightarrow &24x
& = &-14\\\Leftrightarrow & \color{red}{24}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}}
& = & \frac{-14}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{12} } & & \\ & V = \left\{ \frac{-7}{12} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-x }
& = & -6 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -6 \color{blue}{+15} \\\Leftrightarrow &-5x
& = &9\\\Leftrightarrow & \color{red}{-5}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+12}& = & -9 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12+2x }
& = & -9 \color{red}{ -2x }\color{blue}{-12+2x } \\\Leftrightarrow & 5x \color{blue}{+2x }
& = & -9 \color{blue}{-12} \\\Leftrightarrow &7x
& = &-21\\\Leftrightarrow & \color{red}{7}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{-21}{7} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+9}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9-x }
& = & -1 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 11x \color{blue}{-x }
& = & -1 \color{blue}{-9} \\\Leftrightarrow &10x
& = &-10\\\Leftrightarrow & \color{red}{10}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{-10}{10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+9}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9-7x }
& = & -8 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & x \color{blue}{-7x }
& = & -8 \color{blue}{-9} \\\Leftrightarrow &-6x
& = &-17\\\Leftrightarrow & \color{red}{-6}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)