Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(5x-15=-15-14x\)
- \(11x-7=-2+13x\)
- \(7x-2=-13-13x\)
- \(2x+5=11+3x\)
- \(-4x-8=-4+9x\)
- \(-13x-9=14+14x\)
- \(-11x-10=13+14x\)
- \(12x+12=5-11x\)
- \(4x+15=11-7x\)
- \(2x-1=-2+7x\)
- \(-5x+11=-11+x\)
- \(-3x+12=8+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 5x \color{red}{-15}& = & -15 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-15}\color{blue}{+15+14x }
& = & -15 \color{red}{ -14x }\color{blue}{+15+14x } \\\Leftrightarrow & 5x \color{blue}{+14x }
& = & -15 \color{blue}{+15} \\\Leftrightarrow &19x
& = &0\\\Leftrightarrow & \color{red}{19}x
& = &0\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{0}{19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-7}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7-13x }
& = & -2 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & 11x \color{blue}{-13x }
& = & -2 \color{blue}{+7} \\\Leftrightarrow &-2x
& = &5\\\Leftrightarrow & \color{red}{-2}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}}
& = & \frac{5}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-2}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2+13x }
& = & -13 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 7x \color{blue}{+13x }
& = & -13 \color{blue}{+2} \\\Leftrightarrow &20x
& = &-11\\\Leftrightarrow & \color{red}{20}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{-11}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{20} } & & \\ & V = \left\{ \frac{-11}{20} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+5}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+5}\color{blue}{-5-3x }
& = & 11 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & 2x \color{blue}{-3x }
& = & 11 \color{blue}{-5} \\\Leftrightarrow &-x
& = &6\\\Leftrightarrow & \color{red}{-}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{6}{-1} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-8}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-9x }
& = & -4 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & -4x \color{blue}{-9x }
& = & -4 \color{blue}{+8} \\\Leftrightarrow &-13x
& = &4\\\Leftrightarrow & \color{red}{-13}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-9}& = & 14 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-14x }
& = & 14 \color{red}{ +14x }\color{blue}{+9-14x } \\\Leftrightarrow & -13x \color{blue}{-14x }
& = & 14 \color{blue}{+9} \\\Leftrightarrow &-27x
& = &23\\\Leftrightarrow & \color{red}{-27}x
& = &23\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}}
& = & \frac{23}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{27} } & & \\ & V = \left\{ \frac{-23}{27} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-10}& = & 13 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-14x }
& = & 13 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & -11x \color{blue}{-14x }
& = & 13 \color{blue}{+10} \\\Leftrightarrow &-25x
& = &23\\\Leftrightarrow & \color{red}{-25}x
& = &23\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{23}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{25} } & & \\ & V = \left\{ \frac{-23}{25} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+12}& = & 5 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12+11x }
& = & 5 \color{red}{ -11x }\color{blue}{-12+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & 5 \color{blue}{-12} \\\Leftrightarrow &23x
& = &-7\\\Leftrightarrow & \color{red}{23}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-7}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{23} } & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+15}& = & 11 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15+7x }
& = & 11 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & 4x \color{blue}{+7x }
& = & 11 \color{blue}{-15} \\\Leftrightarrow &11x
& = &-4\\\Leftrightarrow & \color{red}{11}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-1}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1-7x }
& = & -2 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & 2x \color{blue}{-7x }
& = & -2 \color{blue}{+1} \\\Leftrightarrow &-5x
& = &-1\\\Leftrightarrow & \color{red}{-5}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+11}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-x }
& = & -11 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & -11 \color{blue}{-11} \\\Leftrightarrow &-6x
& = &-22\\\Leftrightarrow & \color{red}{-6}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+12}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12-x }
& = & 8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 8 \color{blue}{-12} \\\Leftrightarrow &-4x
& = &-4\\\Leftrightarrow & \color{red}{-4}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)