Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(11x-2=4+x\)
- \(-12x-14=-6+5x\)
- \(-x-8=10+0x\)
- \(-14x-9=-5+x\)
- \(-11x-1=5+x\)
- \(-7x+1=-5+11x\)
- \(-3x+15=2+x\)
- \(11x-15=7+4x\)
- \(x-15=10-6x\)
- \(-x-7=5+4x\)
- \(13x+2=-3-12x\)
- \(-5x-1=2+11x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 11x \color{red}{-2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2-x }
& = & 4 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 11x \color{blue}{-x }
& = & 4 \color{blue}{+2} \\\Leftrightarrow &10x
& = &6\\\Leftrightarrow & \color{red}{10}x
& = &6\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{6}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-14}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14-5x }
& = & -6 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & -12x \color{blue}{-5x }
& = & -6 \color{blue}{+14} \\\Leftrightarrow &-17x
& = &8\\\Leftrightarrow & \color{red}{-17}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{17} } & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-8}& = & 10 \color{red}{ +0x } \\\Leftrightarrow & -x \color{red}{-8}\color{blue}{+8+0x }
& = & 10 \color{red}{ +0x }\color{blue}{+8+0x } \\\Leftrightarrow & -x \color{blue}{+0x }
& = & 10 \color{blue}{+8} \\\Leftrightarrow &-x
& = &18\\\Leftrightarrow & \color{red}{-}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{18}{-1} \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-9}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-x }
& = & -5 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -5 \color{blue}{+9} \\\Leftrightarrow &-15x
& = &4\\\Leftrightarrow & \color{red}{-15}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-x }
& = & 5 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 5 \color{blue}{+1} \\\Leftrightarrow &-12x
& = &6\\\Leftrightarrow & \color{red}{-12}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+1}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-11x }
& = & -5 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & -7x \color{blue}{-11x }
& = & -5 \color{blue}{-1} \\\Leftrightarrow &-18x
& = &-6\\\Leftrightarrow & \color{red}{-18}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}}
& = & \frac{-6}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+15}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-x }
& = & 2 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 2 \color{blue}{-15} \\\Leftrightarrow &-4x
& = &-13\\\Leftrightarrow & \color{red}{-4}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-15}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-4x }
& = & 7 \color{red}{ +4x }\color{blue}{+15-4x } \\\Leftrightarrow & 11x \color{blue}{-4x }
& = & 7 \color{blue}{+15} \\\Leftrightarrow &7x
& = &22\\\Leftrightarrow & \color{red}{7}x
& = &22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{22}{7} } & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-15}& = & 10 \color{red}{ -6x } \\\Leftrightarrow & x \color{red}{-15}\color{blue}{+15+6x }
& = & 10 \color{red}{ -6x }\color{blue}{+15+6x } \\\Leftrightarrow & x \color{blue}{+6x }
& = & 10 \color{blue}{+15} \\\Leftrightarrow &7x
& = &25\\\Leftrightarrow & \color{red}{7}x
& = &25\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{25}{7} \\\Leftrightarrow & \color{green}{ x = \frac{25}{7} } & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-7}& = & 5 \color{red}{ +4x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7-4x }
& = & 5 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & -x \color{blue}{-4x }
& = & 5 \color{blue}{+7} \\\Leftrightarrow &-5x
& = &12\\\Leftrightarrow & \color{red}{-5}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+2}& = & -3 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2+12x }
& = & -3 \color{red}{ -12x }\color{blue}{-2+12x } \\\Leftrightarrow & 13x \color{blue}{+12x }
& = & -3 \color{blue}{-2} \\\Leftrightarrow &25x
& = &-5\\\Leftrightarrow & \color{red}{25}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{-5}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-1}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-11x }
& = & 2 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & -5x \color{blue}{-11x }
& = & 2 \color{blue}{+1} \\\Leftrightarrow &-16x
& = &3\\\Leftrightarrow & \color{red}{-16}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{16} } & & \\ & V = \left\{ \frac{-3}{16} \right\} & \\\end{align}\)