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