Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(13x+15=-8+x\)
- \(-13x-10=13+x\)
- \(4x+8=-2+5x\)
- \(-3x+10=15+x\)
- \(-9x+10=5+x\)
- \(6x+2=-13+x\)
- \(11x+4=-10+2x\)
- \(3x+5=-4-2x\)
- \(-x+2=8+8x\)
- \(-10x+7=13+7x\)
- \(7x-6=4-3x\)
- \(11x+14=13-13x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 13x \color{red}{+15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-x }
& = & -8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 13x \color{blue}{-x }
& = & -8 \color{blue}{-15} \\\Leftrightarrow &12x
& = &-23\\\Leftrightarrow & \color{red}{12}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}}
& = & \frac{-23}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{12} } & & \\ & V = \left\{ \frac{-23}{12} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-x }
& = & 13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 13 \color{blue}{+10} \\\Leftrightarrow &-14x
& = &23\\\Leftrightarrow & \color{red}{-14}x
& = &23\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{23}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{14} } & & \\ & V = \left\{ \frac{-23}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+8}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8-5x }
& = & -2 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & 4x \color{blue}{-5x }
& = & -2 \color{blue}{-8} \\\Leftrightarrow &-x
& = &-10\\\Leftrightarrow & \color{red}{-}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-10}{-1} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+10}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-x }
& = & 15 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 15 \color{blue}{-10} \\\Leftrightarrow &-4x
& = &5\\\Leftrightarrow & \color{red}{-4}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+10}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-x }
& = & 5 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 5 \color{blue}{-10} \\\Leftrightarrow &-10x
& = &-5\\\Leftrightarrow & \color{red}{-10}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+2}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2-x }
& = & -13 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & -13 \color{blue}{-2} \\\Leftrightarrow &5x
& = &-15\\\Leftrightarrow & \color{red}{5}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+4}& = & -10 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4-2x }
& = & -10 \color{red}{ +2x }\color{blue}{-4-2x } \\\Leftrightarrow & 11x \color{blue}{-2x }
& = & -10 \color{blue}{-4} \\\Leftrightarrow &9x
& = &-14\\\Leftrightarrow & \color{red}{9}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-14}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+5}& = & -4 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5+2x }
& = & -4 \color{red}{ -2x }\color{blue}{-5+2x } \\\Leftrightarrow & 3x \color{blue}{+2x }
& = & -4 \color{blue}{-5} \\\Leftrightarrow &5x
& = &-9\\\Leftrightarrow & \color{red}{5}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+2}& = & 8 \color{red}{ +8x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2-8x }
& = & 8 \color{red}{ +8x }\color{blue}{-2-8x } \\\Leftrightarrow & -x \color{blue}{-8x }
& = & 8 \color{blue}{-2} \\\Leftrightarrow &-9x
& = &6\\\Leftrightarrow & \color{red}{-9}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+7}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-7x }
& = & 13 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & -10x \color{blue}{-7x }
& = & 13 \color{blue}{-7} \\\Leftrightarrow &-17x
& = &6\\\Leftrightarrow & \color{red}{-17}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-6}& = & 4 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6+3x }
& = & 4 \color{red}{ -3x }\color{blue}{+6+3x } \\\Leftrightarrow & 7x \color{blue}{+3x }
& = & 4 \color{blue}{+6} \\\Leftrightarrow &10x
& = &10\\\Leftrightarrow & \color{red}{10}x
& = &10\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{10}{10} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+14}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14+13x }
& = & 13 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & 11x \color{blue}{+13x }
& = & 13 \color{blue}{-14} \\\Leftrightarrow &24x
& = &-1\\\Leftrightarrow & \color{red}{24}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}}
& = & \frac{-1}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{24} } & & \\ & V = \left\{ \frac{-1}{24} \right\} & \\\end{align}\)