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