Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-11x-15=-1+9x\)
- \(-3x-10=11+7x\)
- \(5x-3=-11+8x\)
- \(-5x+4=-2+x\)
- \(-13x-7=-15+7x\)
- \(11x+3=12+5x\)
- \(4x+1=1-11x\)
- \(10x+9=-4+7x\)
- \(15x+13=-3-14x\)
- \(3x-15=6+x\)
- \(-15x-4=-9+8x\)
- \(12x-14=13+5x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -11x \color{red}{-15}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-9x }
& = & -1 \color{red}{ +9x }\color{blue}{+15-9x } \\\Leftrightarrow & -11x \color{blue}{-9x }
& = & -1 \color{blue}{+15} \\\Leftrightarrow &-20x
& = &14\\\Leftrightarrow & \color{red}{-20}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{14}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-10}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-10}\color{blue}{+10-7x }
& = & 11 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & -3x \color{blue}{-7x }
& = & 11 \color{blue}{+10} \\\Leftrightarrow &-10x
& = &21\\\Leftrightarrow & \color{red}{-10}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{21}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{10} } & & \\ & V = \left\{ \frac{-21}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-3}& = & -11 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3-8x }
& = & -11 \color{red}{ +8x }\color{blue}{+3-8x } \\\Leftrightarrow & 5x \color{blue}{-8x }
& = & -11 \color{blue}{+3} \\\Leftrightarrow &-3x
& = &-8\\\Leftrightarrow & \color{red}{-3}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+4}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4-x }
& = & -2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & -2 \color{blue}{-4} \\\Leftrightarrow &-6x
& = &-6\\\Leftrightarrow & \color{red}{-6}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-6}{-6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-7}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-7x }
& = & -15 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -13x \color{blue}{-7x }
& = & -15 \color{blue}{+7} \\\Leftrightarrow &-20x
& = &-8\\\Leftrightarrow & \color{red}{-20}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{-8}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+3}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3-5x }
& = & 12 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 11x \color{blue}{-5x }
& = & 12 \color{blue}{-3} \\\Leftrightarrow &6x
& = &9\\\Leftrightarrow & \color{red}{6}x
& = &9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}}
& = & \frac{9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+1}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1+11x }
& = & 1 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 4x \color{blue}{+11x }
& = & 1 \color{blue}{-1} \\\Leftrightarrow &15x
& = &0\\\Leftrightarrow & \color{red}{15}x
& = &0\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{0}{15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+9}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9-7x }
& = & -4 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 10x \color{blue}{-7x }
& = & -4 \color{blue}{-9} \\\Leftrightarrow &3x
& = &-13\\\Leftrightarrow & \color{red}{3}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{-13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+13}& = & -3 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13+14x }
& = & -3 \color{red}{ -14x }\color{blue}{-13+14x } \\\Leftrightarrow & 15x \color{blue}{+14x }
& = & -3 \color{blue}{-13} \\\Leftrightarrow &29x
& = &-16\\\Leftrightarrow & \color{red}{29}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}}
& = & \frac{-16}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{29} } & & \\ & V = \left\{ \frac{-16}{29} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-15}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15-x }
& = & 6 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 3x \color{blue}{-x }
& = & 6 \color{blue}{+15} \\\Leftrightarrow &2x
& = &21\\\Leftrightarrow & \color{red}{2}x
& = &21\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{21}{2} \\\Leftrightarrow & \color{green}{ x = \frac{21}{2} } & & \\ & V = \left\{ \frac{21}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-4}& = & -9 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-8x }
& = & -9 \color{red}{ +8x }\color{blue}{+4-8x } \\\Leftrightarrow & -15x \color{blue}{-8x }
& = & -9 \color{blue}{+4} \\\Leftrightarrow &-23x
& = &-5\\\Leftrightarrow & \color{red}{-23}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{-5}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{5}{23} } & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-14}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14-5x }
& = & 13 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & 12x \color{blue}{-5x }
& = & 13 \color{blue}{+14} \\\Leftrightarrow &7x
& = &27\\\Leftrightarrow & \color{red}{7}x
& = &27\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{27}{7} \\\Leftrightarrow & \color{green}{ x = \frac{27}{7} } & & \\ & V = \left\{ \frac{27}{7} \right\} & \\\end{align}\)