Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-3x-10=-12+4x\)
- \(x-6=6-15x\)
- \(7x-8=-1+6x\)
- \(-9x+6=15+x\)
- \(-6x-7=-10+13x\)
- \(-8x-4=14+11x\)
- \(-4x+14=9+x\)
- \(-9x-12=-12+14x\)
- \(-10x-10=7+x\)
- \(-10x-9=9+x\)
- \(-8x-4=1+x\)
- \(-8x+6=-3+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -3x \color{red}{-10}& = & -12 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-10}\color{blue}{+10-4x }
& = & -12 \color{red}{ +4x }\color{blue}{+10-4x } \\\Leftrightarrow & -3x \color{blue}{-4x }
& = & -12 \color{blue}{+10} \\\Leftrightarrow &-7x
& = &-2\\\Leftrightarrow & \color{red}{-7}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-6}& = & 6 \color{red}{ -15x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6+15x }
& = & 6 \color{red}{ -15x }\color{blue}{+6+15x } \\\Leftrightarrow & x \color{blue}{+15x }
& = & 6 \color{blue}{+6} \\\Leftrightarrow &16x
& = &12\\\Leftrightarrow & \color{red}{16}x
& = &12\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}}
& = & \frac{12}{16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-8}& = & -1 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8-6x }
& = & -1 \color{red}{ +6x }\color{blue}{+8-6x } \\\Leftrightarrow & 7x \color{blue}{-6x }
& = & -1 \color{blue}{+8} \\\Leftrightarrow &x
& = &7\\\Leftrightarrow & \color{red}{}x
& = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+6}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-x }
& = & 15 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 15 \color{blue}{-6} \\\Leftrightarrow &-10x
& = &9\\\Leftrightarrow & \color{red}{-10}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-7}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-13x }
& = & -10 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & -10 \color{blue}{+7} \\\Leftrightarrow &-19x
& = &-3\\\Leftrightarrow & \color{red}{-19}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-4}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-11x }
& = & 14 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & -8x \color{blue}{-11x }
& = & 14 \color{blue}{+4} \\\Leftrightarrow &-19x
& = &18\\\Leftrightarrow & \color{red}{-19}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{18}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{19} } & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+14}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14-x }
& = & 9 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & 9 \color{blue}{-14} \\\Leftrightarrow &-5x
& = &-5\\\Leftrightarrow & \color{red}{-5}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-5}{-5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-12}& = & -12 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-14x }
& = & -12 \color{red}{ +14x }\color{blue}{+12-14x } \\\Leftrightarrow & -9x \color{blue}{-14x }
& = & -12 \color{blue}{+12} \\\Leftrightarrow &-23x
& = &0\\\Leftrightarrow & \color{red}{-23}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{0}{-23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-10}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x }
& = & 7 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 7 \color{blue}{+10} \\\Leftrightarrow &-11x
& = &17\\\Leftrightarrow & \color{red}{-11}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-x }
& = & 9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 9 \color{blue}{+9} \\\Leftrightarrow &-11x
& = &18\\\Leftrightarrow & \color{red}{-11}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-4}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-x }
& = & 1 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 1 \color{blue}{+4} \\\Leftrightarrow &-9x
& = &5\\\Leftrightarrow & \color{red}{-9}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-x }
& = & -3 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & -3 \color{blue}{-6} \\\Leftrightarrow &-9x
& = &-9\\\Leftrightarrow & \color{red}{-9}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-9}{-9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)