Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-15x-8=-14+x\)
- \(14x+5=-1+x\)
- \(-7x+5=-12+x\)
- \(-3x+14=8+10x\)
- \(15x+9=-5+11x\)
- \(12x+6=8-7x\)
- \(-11x+12=-9+x\)
- \(11x-7=3+4x\)
- \(15x-9=12-11x\)
- \(3x+12=4-11x\)
- \(-10x+12=-9+x\)
- \(-x-8=-4-7x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -15x \color{red}{-8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-x }
& = & -14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & -14 \color{blue}{+8} \\\Leftrightarrow &-16x
& = &-6\\\Leftrightarrow & \color{red}{-16}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5-x }
& = & -1 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & -1 \color{blue}{-5} \\\Leftrightarrow &13x
& = &-6\\\Leftrightarrow & \color{red}{13}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+5}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-x }
& = & -12 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -12 \color{blue}{-5} \\\Leftrightarrow &-8x
& = &-17\\\Leftrightarrow & \color{red}{-8}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{17}{8} } & & \\ & V = \left\{ \frac{17}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+14}& = & 8 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14-10x }
& = & 8 \color{red}{ +10x }\color{blue}{-14-10x } \\\Leftrightarrow & -3x \color{blue}{-10x }
& = & 8 \color{blue}{-14} \\\Leftrightarrow &-13x
& = &-6\\\Leftrightarrow & \color{red}{-13}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+9}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9-11x }
& = & -5 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & 15x \color{blue}{-11x }
& = & -5 \color{blue}{-9} \\\Leftrightarrow &4x
& = &-14\\\Leftrightarrow & \color{red}{4}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{-14}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+6}& = & 8 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6+7x }
& = & 8 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 12x \color{blue}{+7x }
& = & 8 \color{blue}{-6} \\\Leftrightarrow &19x
& = &2\\\Leftrightarrow & \color{red}{19}x
& = &2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{2}{19} } & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+12}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-x }
& = & -9 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -9 \color{blue}{-12} \\\Leftrightarrow &-12x
& = &-21\\\Leftrightarrow & \color{red}{-12}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-21}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-7}& = & 3 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7-4x }
& = & 3 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & 11x \color{blue}{-4x }
& = & 3 \color{blue}{+7} \\\Leftrightarrow &7x
& = &10\\\Leftrightarrow & \color{red}{7}x
& = &10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-9}& = & 12 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9+11x }
& = & 12 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 15x \color{blue}{+11x }
& = & 12 \color{blue}{+9} \\\Leftrightarrow &26x
& = &21\\\Leftrightarrow & \color{red}{26}x
& = &21\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}}
& = & \frac{21}{26} \\\Leftrightarrow & \color{green}{ x = \frac{21}{26} } & & \\ & V = \left\{ \frac{21}{26} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+12}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12+11x }
& = & 4 \color{red}{ -11x }\color{blue}{-12+11x } \\\Leftrightarrow & 3x \color{blue}{+11x }
& = & 4 \color{blue}{-12} \\\Leftrightarrow &14x
& = &-8\\\Leftrightarrow & \color{red}{14}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{-8}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+12}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12-x }
& = & -9 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -9 \color{blue}{-12} \\\Leftrightarrow &-11x
& = &-21\\\Leftrightarrow & \color{red}{-11}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-8}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{-8}\color{blue}{+8+7x }
& = & -4 \color{red}{ -7x }\color{blue}{+8+7x } \\\Leftrightarrow & -x \color{blue}{+7x }
& = & -4 \color{blue}{+8} \\\Leftrightarrow &6x
& = &4\\\Leftrightarrow & \color{red}{6}x
& = &4\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}}
& = & \frac{4}{6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)