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