Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(15x+3=-14-11x\)
- \(15x+15=-15-2x\)
- \(-8x+11=-13+9x\)
- \(-15x-7=-11+x\)
- \(3x-1=5-2x\)
- \(-9x+4=10+x\)
- \(-12x+2=13+x\)
- \(8x+11=-11+x\)
- \(-8x-6=8+x\)
- \(-x+4=2+0x\)
- \(-13x-15=-2+7x\)
- \(2x+10=7+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 15x \color{red}{+3}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3+11x }
& = & -14 \color{red}{ -11x }\color{blue}{-3+11x } \\\Leftrightarrow & 15x \color{blue}{+11x }
& = & -14 \color{blue}{-3} \\\Leftrightarrow &26x
& = &-17\\\Leftrightarrow & \color{red}{26}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}}
& = & \frac{-17}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{26} } & & \\ & V = \left\{ \frac{-17}{26} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+15}& = & -15 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15+2x }
& = & -15 \color{red}{ -2x }\color{blue}{-15+2x } \\\Leftrightarrow & 15x \color{blue}{+2x }
& = & -15 \color{blue}{-15} \\\Leftrightarrow &17x
& = &-30\\\Leftrightarrow & \color{red}{17}x
& = &-30\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-30}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-30}{17} } & & \\ & V = \left\{ \frac{-30}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+11}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-9x }
& = & -13 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & -8x \color{blue}{-9x }
& = & -13 \color{blue}{-11} \\\Leftrightarrow &-17x
& = &-24\\\Leftrightarrow & \color{red}{-17}x
& = &-24\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-24}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{24}{17} } & & \\ & V = \left\{ \frac{24}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-7}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-x }
& = & -11 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & -11 \color{blue}{+7} \\\Leftrightarrow &-16x
& = &-4\\\Leftrightarrow & \color{red}{-16}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-1}& = & 5 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1+2x }
& = & 5 \color{red}{ -2x }\color{blue}{+1+2x } \\\Leftrightarrow & 3x \color{blue}{+2x }
& = & 5 \color{blue}{+1} \\\Leftrightarrow &5x
& = &6\\\Leftrightarrow & \color{red}{5}x
& = &6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+4}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-x }
& = & 10 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 10 \color{blue}{-4} \\\Leftrightarrow &-10x
& = &6\\\Leftrightarrow & \color{red}{-10}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+2}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-x }
& = & 13 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 13 \color{blue}{-2} \\\Leftrightarrow &-13x
& = &11\\\Leftrightarrow & \color{red}{-13}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+11}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11-x }
& = & -11 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 8x \color{blue}{-x }
& = & -11 \color{blue}{-11} \\\Leftrightarrow &7x
& = &-22\\\Leftrightarrow & \color{red}{7}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-6}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6-x }
& = & 8 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 8 \color{blue}{+6} \\\Leftrightarrow &-9x
& = &14\\\Leftrightarrow & \color{red}{-9}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+4}& = & 2 \color{red}{ +0x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4+0x }
& = & 2 \color{red}{ +0x }\color{blue}{-4+0x } \\\Leftrightarrow & -x \color{blue}{+0x }
& = & 2 \color{blue}{-4} \\\Leftrightarrow &-x
& = &-2\\\Leftrightarrow & \color{red}{-}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-2}{-1} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-15}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-7x }
& = & -2 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -13x \color{blue}{-7x }
& = & -2 \color{blue}{+15} \\\Leftrightarrow &-20x
& = &13\\\Leftrightarrow & \color{red}{-20}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{13}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{20} } & & \\ & V = \left\{ \frac{-13}{20} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+10}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-x }
& = & 7 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & 7 \color{blue}{-10} \\\Leftrightarrow &x
& = &-3\\\Leftrightarrow & \color{red}{}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)