Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-15x-7=10+x\)
- \(-2x+2=7+5x\)
- \(-11x+8=-4+14x\)
- \(15x-6=-8-11x\)
- \(x+5=-9+10x\)
- \(-9x+5=-10+5x\)
- \(8x+3=11+3x\)
- \(x-11=8-13x\)
- \(-3x+2=12+x\)
- \(11x-9=-10+10x\)
- \(4x+9=9-7x\)
- \(7x-3=3+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -15x \color{red}{-7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-x }
& = & 10 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & 10 \color{blue}{+7} \\\Leftrightarrow &-16x
& = &17\\\Leftrightarrow & \color{red}{-16}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{16} } & & \\ & V = \left\{ \frac{-17}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+2}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2-5x }
& = & 7 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & -2x \color{blue}{-5x }
& = & 7 \color{blue}{-2} \\\Leftrightarrow &-7x
& = &5\\\Leftrightarrow & \color{red}{-7}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+8}& = & -4 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8-14x }
& = & -4 \color{red}{ +14x }\color{blue}{-8-14x } \\\Leftrightarrow & -11x \color{blue}{-14x }
& = & -4 \color{blue}{-8} \\\Leftrightarrow &-25x
& = &-12\\\Leftrightarrow & \color{red}{-25}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-12}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{12}{25} } & & \\ & V = \left\{ \frac{12}{25} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-6}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-6}\color{blue}{+6+11x }
& = & -8 \color{red}{ -11x }\color{blue}{+6+11x } \\\Leftrightarrow & 15x \color{blue}{+11x }
& = & -8 \color{blue}{+6} \\\Leftrightarrow &26x
& = &-2\\\Leftrightarrow & \color{red}{26}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}}
& = & \frac{-2}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+5}& = & -9 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5-10x }
& = & -9 \color{red}{ +10x }\color{blue}{-5-10x } \\\Leftrightarrow & x \color{blue}{-10x }
& = & -9 \color{blue}{-5} \\\Leftrightarrow &-9x
& = &-14\\\Leftrightarrow & \color{red}{-9}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+5}& = & -10 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-5x }
& = & -10 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & -9x \color{blue}{-5x }
& = & -10 \color{blue}{-5} \\\Leftrightarrow &-14x
& = &-15\\\Leftrightarrow & \color{red}{-14}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{14} } & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+3}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3-3x }
& = & 11 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & 8x \color{blue}{-3x }
& = & 11 \color{blue}{-3} \\\Leftrightarrow &5x
& = &8\\\Leftrightarrow & \color{red}{5}x
& = &8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-11}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11+13x }
& = & 8 \color{red}{ -13x }\color{blue}{+11+13x } \\\Leftrightarrow & x \color{blue}{+13x }
& = & 8 \color{blue}{+11} \\\Leftrightarrow &14x
& = &19\\\Leftrightarrow & \color{red}{14}x
& = &19\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{19}{14} \\\Leftrightarrow & \color{green}{ x = \frac{19}{14} } & & \\ & V = \left\{ \frac{19}{14} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x }
& = & 12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 12 \color{blue}{-2} \\\Leftrightarrow &-4x
& = &10\\\Leftrightarrow & \color{red}{-4}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-9}& = & -10 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9-10x }
& = & -10 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & 11x \color{blue}{-10x }
& = & -10 \color{blue}{+9} \\\Leftrightarrow &x
& = &-1\\\Leftrightarrow & \color{red}{}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+9}& = & 9 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9+7x }
& = & 9 \color{red}{ -7x }\color{blue}{-9+7x } \\\Leftrightarrow & 4x \color{blue}{+7x }
& = & 9 \color{blue}{-9} \\\Leftrightarrow &11x
& = &0\\\Leftrightarrow & \color{red}{11}x
& = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3-x }
& = & 3 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 7x \color{blue}{-x }
& = & 3 \color{blue}{+3} \\\Leftrightarrow &6x
& = &6\\\Leftrightarrow & \color{red}{6}x
& = &6\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}}
& = & \frac{6}{6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)