Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-15x+1=5+x\)
- \(-12x-15=2+x\)
- \(-9x-14=6+x\)
- \(-7x+7=-4+x\)
- \(6x+6=-10-11x\)
- \(15x+9=-9-14x\)
- \(-15x+4=12+4x\)
- \(-13x+4=-1+x\)
- \(-3x-10=3+10x\)
- \(2x+8=3+x\)
- \(-15x+14=-13+13x\)
- \(14x-3=-5-13x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -15x \color{red}{+1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-x }
& = & 5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & 5 \color{blue}{-1} \\\Leftrightarrow &-16x
& = &4\\\Leftrightarrow & \color{red}{-16}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-15}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15-x }
& = & 2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 2 \color{blue}{+15} \\\Leftrightarrow &-13x
& = &17\\\Leftrightarrow & \color{red}{-13}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-14}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-x }
& = & 6 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 6 \color{blue}{+14} \\\Leftrightarrow &-10x
& = &20\\\Leftrightarrow & \color{red}{-10}x
& = &20\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{20}{-10} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+7}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7-x }
& = & -4 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -4 \color{blue}{-7} \\\Leftrightarrow &-8x
& = &-11\\\Leftrightarrow & \color{red}{-8}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+6}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6+11x }
& = & -10 \color{red}{ -11x }\color{blue}{-6+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & -10 \color{blue}{-6} \\\Leftrightarrow &17x
& = &-16\\\Leftrightarrow & \color{red}{17}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+9}& = & -9 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9+14x }
& = & -9 \color{red}{ -14x }\color{blue}{-9+14x } \\\Leftrightarrow & 15x \color{blue}{+14x }
& = & -9 \color{blue}{-9} \\\Leftrightarrow &29x
& = &-18\\\Leftrightarrow & \color{red}{29}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}}
& = & \frac{-18}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{29} } & & \\ & V = \left\{ \frac{-18}{29} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+4}& = & 12 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-4x }
& = & 12 \color{red}{ +4x }\color{blue}{-4-4x } \\\Leftrightarrow & -15x \color{blue}{-4x }
& = & 12 \color{blue}{-4} \\\Leftrightarrow &-19x
& = &8\\\Leftrightarrow & \color{red}{-19}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{8}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+4}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x }
& = & -1 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -1 \color{blue}{-4} \\\Leftrightarrow &-14x
& = &-5\\\Leftrightarrow & \color{red}{-14}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-10}& = & 3 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-10}\color{blue}{+10-10x }
& = & 3 \color{red}{ +10x }\color{blue}{+10-10x } \\\Leftrightarrow & -3x \color{blue}{-10x }
& = & 3 \color{blue}{+10} \\\Leftrightarrow &-13x
& = &13\\\Leftrightarrow & \color{red}{-13}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{13}{-13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+8}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-x }
& = & 3 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & 3 \color{blue}{-8} \\\Leftrightarrow &x
& = &-5\\\Leftrightarrow & \color{red}{}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+14}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-13x }
& = & -13 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & -13 \color{blue}{-14} \\\Leftrightarrow &-28x
& = &-27\\\Leftrightarrow & \color{red}{-28}x
& = &-27\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{-27}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{27}{28} } & & \\ & V = \left\{ \frac{27}{28} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-3}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3+13x }
& = & -5 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 14x \color{blue}{+13x }
& = & -5 \color{blue}{+3} \\\Leftrightarrow &27x
& = &-2\\\Leftrightarrow & \color{red}{27}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}}
& = & \frac{-2}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{27} } & & \\ & V = \left\{ \frac{-2}{27} \right\} & \\\end{align}\)