Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-9x-5=3+x\)
- \(5x-3=-15-14x\)
- \(6x+14=4-11x\)
- \(13x+12=15-6x\)
- \(-11x+7=10+x\)
- \(x-3=-7+13x\)
- \(-3x-12=-15+4x\)
- \(2x+8=-9+x\)
- \(11x+6=5-8x\)
- \(-3x-3=-8+13x\)
- \(10x-9=-7+x\)
- \(2x-14=15+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -9x \color{red}{-5}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-x }
& = & 3 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 3 \color{blue}{+5} \\\Leftrightarrow &-10x
& = &8\\\Leftrightarrow & \color{red}{-10}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-3}& = & -15 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3+14x }
& = & -15 \color{red}{ -14x }\color{blue}{+3+14x } \\\Leftrightarrow & 5x \color{blue}{+14x }
& = & -15 \color{blue}{+3} \\\Leftrightarrow &19x
& = &-12\\\Leftrightarrow & \color{red}{19}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-12}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{19} } & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+14}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14+11x }
& = & 4 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & 4 \color{blue}{-14} \\\Leftrightarrow &17x
& = &-10\\\Leftrightarrow & \color{red}{17}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+12}& = & 15 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12+6x }
& = & 15 \color{red}{ -6x }\color{blue}{-12+6x } \\\Leftrightarrow & 13x \color{blue}{+6x }
& = & 15 \color{blue}{-12} \\\Leftrightarrow &19x
& = &3\\\Leftrightarrow & \color{red}{19}x
& = &3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-x }
& = & 10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 10 \color{blue}{-7} \\\Leftrightarrow &-12x
& = &3\\\Leftrightarrow & \color{red}{-12}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-3}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3-13x }
& = & -7 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & x \color{blue}{-13x }
& = & -7 \color{blue}{+3} \\\Leftrightarrow &-12x
& = &-4\\\Leftrightarrow & \color{red}{-12}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-12}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12-4x }
& = & -15 \color{red}{ +4x }\color{blue}{+12-4x } \\\Leftrightarrow & -3x \color{blue}{-4x }
& = & -15 \color{blue}{+12} \\\Leftrightarrow &-7x
& = &-3\\\Leftrightarrow & \color{red}{-7}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+8}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-x }
& = & -9 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & -9 \color{blue}{-8} \\\Leftrightarrow &x
& = &-17\\\Leftrightarrow & \color{red}{}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -17 \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+6}& = & 5 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6+8x }
& = & 5 \color{red}{ -8x }\color{blue}{-6+8x } \\\Leftrightarrow & 11x \color{blue}{+8x }
& = & 5 \color{blue}{-6} \\\Leftrightarrow &19x
& = &-1\\\Leftrightarrow & \color{red}{19}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-3}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-13x }
& = & -8 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -3x \color{blue}{-13x }
& = & -8 \color{blue}{+3} \\\Leftrightarrow &-16x
& = &-5\\\Leftrightarrow & \color{red}{-16}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9-x }
& = & -7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 10x \color{blue}{-x }
& = & -7 \color{blue}{+9} \\\Leftrightarrow &9x
& = &2\\\Leftrightarrow & \color{red}{9}x
& = &2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-14}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-x }
& = & 15 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & 15 \color{blue}{+14} \\\Leftrightarrow &x
& = &29\\\Leftrightarrow & \color{red}{}x
& = &29\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 29 \\\Leftrightarrow & \color{green}{ x = 29 } & & \\ & V = \left\{ 29 \right\} & \\\end{align}\)