Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-15x-12=-10+x\)
- \(15x-11=2-2x\)
- \(10x+15=7+x\)
- \(2x-5=-2+11x\)
- \(13x+5=6+12x\)
- \(-3x-14=-2+x\)
- \(6x-3=1-11x\)
- \(10x+5=-5-13x\)
- \(2x-11=2+x\)
- \(-9x-10=6+7x\)
- \(14x-9=1-13x\)
- \(-8x+12=14+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -15x \color{red}{-12}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-x }
& = & -10 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & -10 \color{blue}{+12} \\\Leftrightarrow &-16x
& = &2\\\Leftrightarrow & \color{red}{-16}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-11}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11+2x }
& = & 2 \color{red}{ -2x }\color{blue}{+11+2x } \\\Leftrightarrow & 15x \color{blue}{+2x }
& = & 2 \color{blue}{+11} \\\Leftrightarrow &17x
& = &13\\\Leftrightarrow & \color{red}{17}x
& = &13\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{13}{17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+15}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15-x }
& = & 7 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 10x \color{blue}{-x }
& = & 7 \color{blue}{-15} \\\Leftrightarrow &9x
& = &-8\\\Leftrightarrow & \color{red}{9}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-5}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-11x }
& = & -2 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & 2x \color{blue}{-11x }
& = & -2 \color{blue}{+5} \\\Leftrightarrow &-9x
& = &3\\\Leftrightarrow & \color{red}{-9}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+5}& = & 6 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5-12x }
& = & 6 \color{red}{ +12x }\color{blue}{-5-12x } \\\Leftrightarrow & 13x \color{blue}{-12x }
& = & 6 \color{blue}{-5} \\\Leftrightarrow &x
& = &1\\\Leftrightarrow & \color{red}{}x
& = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-14}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-x }
& = & -2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -2 \color{blue}{+14} \\\Leftrightarrow &-4x
& = &12\\\Leftrightarrow & \color{red}{-4}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-3}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3+11x }
& = & 1 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & 1 \color{blue}{+3} \\\Leftrightarrow &17x
& = &4\\\Leftrightarrow & \color{red}{17}x
& = &4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+5}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5+13x }
& = & -5 \color{red}{ -13x }\color{blue}{-5+13x } \\\Leftrightarrow & 10x \color{blue}{+13x }
& = & -5 \color{blue}{-5} \\\Leftrightarrow &23x
& = &-10\\\Leftrightarrow & \color{red}{23}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-10}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{23} } & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-11}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-x }
& = & 2 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & 2 \color{blue}{+11} \\\Leftrightarrow &x
& = &13\\\Leftrightarrow & \color{red}{}x
& = &13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 13 \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-10}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-7x }
& = & 6 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & -9x \color{blue}{-7x }
& = & 6 \color{blue}{+10} \\\Leftrightarrow &-16x
& = &16\\\Leftrightarrow & \color{red}{-16}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{16}{-16} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-9}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9+13x }
& = & 1 \color{red}{ -13x }\color{blue}{+9+13x } \\\Leftrightarrow & 14x \color{blue}{+13x }
& = & 1 \color{blue}{+9} \\\Leftrightarrow &27x
& = &10\\\Leftrightarrow & \color{red}{27}x
& = &10\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}}
& = & \frac{10}{27} \\\Leftrightarrow & \color{green}{ x = \frac{10}{27} } & & \\ & V = \left\{ \frac{10}{27} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+12}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-x }
& = & 14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 14 \color{blue}{-12} \\\Leftrightarrow &-9x
& = &2\\\Leftrightarrow & \color{red}{-9}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)