Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(4x-14=-9+9x\)
- \(13x+14=-4+10x\)
- \(-10x+11=-14+x\)
- \(2x+11=6+x\)
- \(-8x+7=-13+9x\)
- \(-x-6=8-5x\)
- \(-6x+1=-11+x\)
- \(2x+8=-3+7x\)
- \(-15x+4=-3+x\)
- \(7x-15=-8-6x\)
- \(7x-9=2-3x\)
- \(13x+15=-5+6x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 4x \color{red}{-14}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14-9x }
& = & -9 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & 4x \color{blue}{-9x }
& = & -9 \color{blue}{+14} \\\Leftrightarrow &-5x
& = &5\\\Leftrightarrow & \color{red}{-5}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+14}& = & -4 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14-10x }
& = & -4 \color{red}{ +10x }\color{blue}{-14-10x } \\\Leftrightarrow & 13x \color{blue}{-10x }
& = & -4 \color{blue}{-14} \\\Leftrightarrow &3x
& = &-18\\\Leftrightarrow & \color{red}{3}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{-18}{3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-x }
& = & -14 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -14 \color{blue}{-11} \\\Leftrightarrow &-11x
& = &-25\\\Leftrightarrow & \color{red}{-11}x
& = &-25\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-25}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{25}{11} } & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+11}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11-x }
& = & 6 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & 6 \color{blue}{-11} \\\Leftrightarrow &x
& = &-5\\\Leftrightarrow & \color{red}{}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+7}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-9x }
& = & -13 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & -8x \color{blue}{-9x }
& = & -13 \color{blue}{-7} \\\Leftrightarrow &-17x
& = &-20\\\Leftrightarrow & \color{red}{-17}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-20}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{20}{17} } & & \\ & V = \left\{ \frac{20}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-6}& = & 8 \color{red}{ -5x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6+5x }
& = & 8 \color{red}{ -5x }\color{blue}{+6+5x } \\\Leftrightarrow & -x \color{blue}{+5x }
& = & 8 \color{blue}{+6} \\\Leftrightarrow &4x
& = &14\\\Leftrightarrow & \color{red}{4}x
& = &14\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{14}{4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+1}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-x }
& = & -11 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -11 \color{blue}{-1} \\\Leftrightarrow &-7x
& = &-12\\\Leftrightarrow & \color{red}{-7}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+8}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-7x }
& = & -3 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & 2x \color{blue}{-7x }
& = & -3 \color{blue}{-8} \\\Leftrightarrow &-5x
& = &-11\\\Leftrightarrow & \color{red}{-5}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-x }
& = & -3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & -3 \color{blue}{-4} \\\Leftrightarrow &-16x
& = &-7\\\Leftrightarrow & \color{red}{-16}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-15}& = & -8 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+6x }
& = & -8 \color{red}{ -6x }\color{blue}{+15+6x } \\\Leftrightarrow & 7x \color{blue}{+6x }
& = & -8 \color{blue}{+15} \\\Leftrightarrow &13x
& = &7\\\Leftrightarrow & \color{red}{13}x
& = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-9}& = & 2 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9+3x }
& = & 2 \color{red}{ -3x }\color{blue}{+9+3x } \\\Leftrightarrow & 7x \color{blue}{+3x }
& = & 2 \color{blue}{+9} \\\Leftrightarrow &10x
& = &11\\\Leftrightarrow & \color{red}{10}x
& = &11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+15}& = & -5 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-6x }
& = & -5 \color{red}{ +6x }\color{blue}{-15-6x } \\\Leftrightarrow & 13x \color{blue}{-6x }
& = & -5 \color{blue}{-15} \\\Leftrightarrow &7x
& = &-20\\\Leftrightarrow & \color{red}{7}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{-20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{7} } & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)