Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(7x-1=13-10x\)
- \(-x-4=9+11x\)
- \(15x+13=8+7x\)
- \(7x-10=-1-6x\)
- \(12x-9=-11-11x\)
- \(-14x+9=-2+x\)
- \(-8x-4=4+x\)
- \(-3x+10=7+x\)
- \(-12x+9=-11+x\)
- \(3x+9=6+x\)
- \(-x-3=-8+15x\)
- \(10x+1=2+3x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 7x \color{red}{-1}& = & 13 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1+10x }
& = & 13 \color{red}{ -10x }\color{blue}{+1+10x } \\\Leftrightarrow & 7x \color{blue}{+10x }
& = & 13 \color{blue}{+1} \\\Leftrightarrow &17x
& = &14\\\Leftrightarrow & \color{red}{17}x
& = &14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-4}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4-11x }
& = & 9 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & -x \color{blue}{-11x }
& = & 9 \color{blue}{+4} \\\Leftrightarrow &-12x
& = &13\\\Leftrightarrow & \color{red}{-12}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+13}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13-7x }
& = & 8 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & 15x \color{blue}{-7x }
& = & 8 \color{blue}{-13} \\\Leftrightarrow &8x
& = &-5\\\Leftrightarrow & \color{red}{8}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{-5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-10}& = & -1 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10+6x }
& = & -1 \color{red}{ -6x }\color{blue}{+10+6x } \\\Leftrightarrow & 7x \color{blue}{+6x }
& = & -1 \color{blue}{+10} \\\Leftrightarrow &13x
& = &9\\\Leftrightarrow & \color{red}{13}x
& = &9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-9}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9+11x }
& = & -11 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & -11 \color{blue}{+9} \\\Leftrightarrow &23x
& = &-2\\\Leftrightarrow & \color{red}{23}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{23} } & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+9}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9-x }
& = & -2 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -2 \color{blue}{-9} \\\Leftrightarrow &-15x
& = &-11\\\Leftrightarrow & \color{red}{-15}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{11}{15} } & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-x }
& = & 4 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 4 \color{blue}{+4} \\\Leftrightarrow &-9x
& = &8\\\Leftrightarrow & \color{red}{-9}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{8}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+10}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-x }
& = & 7 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 7 \color{blue}{-10} \\\Leftrightarrow &-4x
& = &-3\\\Leftrightarrow & \color{red}{-4}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+9}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+9}\color{blue}{-9-x }
& = & -11 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -11 \color{blue}{-9} \\\Leftrightarrow &-13x
& = &-20\\\Leftrightarrow & \color{red}{-13}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+9}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9-x }
& = & 6 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 3x \color{blue}{-x }
& = & 6 \color{blue}{-9} \\\Leftrightarrow &2x
& = &-3\\\Leftrightarrow & \color{red}{2}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{-3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-3}& = & -8 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3-15x }
& = & -8 \color{red}{ +15x }\color{blue}{+3-15x } \\\Leftrightarrow & -x \color{blue}{-15x }
& = & -8 \color{blue}{+3} \\\Leftrightarrow &-16x
& = &-5\\\Leftrightarrow & \color{red}{-16}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+1}& = & 2 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1-3x }
& = & 2 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & 10x \color{blue}{-3x }
& = & 2 \color{blue}{-1} \\\Leftrightarrow &7x
& = &1\\\Leftrightarrow & \color{red}{7}x
& = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)