Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(3x-15=15-11x\)
- \(-13x+1=6+x\)
- \(11x+15=9-13x\)
- \(-7x+9=14+x\)
- \(4x-11=-4+11x\)
- \(-12x+14=12+5x\)
- \(-7x-14=4+x\)
- \(-12x+15=11+13x\)
- \(4x-3=-8-3x\)
- \(-13x-3=13+7x\)
- \(-x-4=14+13x\)
- \(-13x+4=-13+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 3x \color{red}{-15}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15+11x }
& = & 15 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 3x \color{blue}{+11x }
& = & 15 \color{blue}{+15} \\\Leftrightarrow &14x
& = &30\\\Leftrightarrow & \color{red}{14}x
& = &30\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{30}{14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{7} } & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1-x }
& = & 6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 6 \color{blue}{-1} \\\Leftrightarrow &-14x
& = &5\\\Leftrightarrow & \color{red}{-14}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+15}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15+13x }
& = & 9 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 11x \color{blue}{+13x }
& = & 9 \color{blue}{-15} \\\Leftrightarrow &24x
& = &-6\\\Leftrightarrow & \color{red}{24}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}}
& = & \frac{-6}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+9}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x }
& = & 14 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & 14 \color{blue}{-9} \\\Leftrightarrow &-8x
& = &5\\\Leftrightarrow & \color{red}{-8}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-11}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-11}\color{blue}{+11-11x }
& = & -4 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 4x \color{blue}{-11x }
& = & -4 \color{blue}{+11} \\\Leftrightarrow &-7x
& = &7\\\Leftrightarrow & \color{red}{-7}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+14}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-5x }
& = & 12 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & -12x \color{blue}{-5x }
& = & 12 \color{blue}{-14} \\\Leftrightarrow &-17x
& = &-2\\\Leftrightarrow & \color{red}{-17}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-x }
& = & 4 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & 4 \color{blue}{+14} \\\Leftrightarrow &-8x
& = &18\\\Leftrightarrow & \color{red}{-8}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{18}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+15}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-13x }
& = & 11 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & 11 \color{blue}{-15} \\\Leftrightarrow &-25x
& = &-4\\\Leftrightarrow & \color{red}{-25}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-4}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{4}{25} } & & \\ & V = \left\{ \frac{4}{25} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-3}& = & -8 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-3}\color{blue}{+3+3x }
& = & -8 \color{red}{ -3x }\color{blue}{+3+3x } \\\Leftrightarrow & 4x \color{blue}{+3x }
& = & -8 \color{blue}{+3} \\\Leftrightarrow &7x
& = &-5\\\Leftrightarrow & \color{red}{7}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-3}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-7x }
& = & 13 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -13x \color{blue}{-7x }
& = & 13 \color{blue}{+3} \\\Leftrightarrow &-20x
& = &16\\\Leftrightarrow & \color{red}{-20}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{16}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-4}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4-13x }
& = & 14 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -x \color{blue}{-13x }
& = & 14 \color{blue}{+4} \\\Leftrightarrow &-14x
& = &18\\\Leftrightarrow & \color{red}{-14}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+4}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x }
& = & -13 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -13 \color{blue}{-4} \\\Leftrightarrow &-14x
& = &-17\\\Leftrightarrow & \color{red}{-14}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-17}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{17}{14} } & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)