Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-3x+10=-3+x\)
- \(2x-13=-1+x\)
- \(14x+5=3+9x\)
- \(-14x-4=9+x\)
- \(-4x+10=12+5x\)
- \(-9x-2=-8+x\)
- \(4x+6=2-7x\)
- \(-8x+14=-14+9x\)
- \(-15x-3=11+x\)
- \(-6x+5=-3+x\)
- \(-4x+3=7+13x\)
- \(3x-7=-14+8x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -3x \color{red}{+10}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-x }
& = & -3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -3 \color{blue}{-10} \\\Leftrightarrow &-4x
& = &-13\\\Leftrightarrow & \color{red}{-4}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-x }
& = & -1 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & -1 \color{blue}{+13} \\\Leftrightarrow &x
& = &12\\\Leftrightarrow & \color{red}{}x
& = &12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 12 \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+5}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5-9x }
& = & 3 \color{red}{ +9x }\color{blue}{-5-9x } \\\Leftrightarrow & 14x \color{blue}{-9x }
& = & 3 \color{blue}{-5} \\\Leftrightarrow &5x
& = &-2\\\Leftrightarrow & \color{red}{5}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-4}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-4}\color{blue}{+4-x }
& = & 9 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 9 \color{blue}{+4} \\\Leftrightarrow &-15x
& = &13\\\Leftrightarrow & \color{red}{-15}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+10}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10-5x }
& = & 12 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & -4x \color{blue}{-5x }
& = & 12 \color{blue}{-10} \\\Leftrightarrow &-9x
& = &2\\\Leftrightarrow & \color{red}{-9}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-2}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-2}\color{blue}{+2-x }
& = & -8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -8 \color{blue}{+2} \\\Leftrightarrow &-10x
& = &-6\\\Leftrightarrow & \color{red}{-10}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+6}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6+7x }
& = & 2 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 4x \color{blue}{+7x }
& = & 2 \color{blue}{-6} \\\Leftrightarrow &11x
& = &-4\\\Leftrightarrow & \color{red}{11}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+14}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-9x }
& = & -14 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & -8x \color{blue}{-9x }
& = & -14 \color{blue}{-14} \\\Leftrightarrow &-17x
& = &-28\\\Leftrightarrow & \color{red}{-17}x
& = &-28\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-28}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{28}{17} } & & \\ & V = \left\{ \frac{28}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-3}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-3}\color{blue}{+3-x }
& = & 11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & 11 \color{blue}{+3} \\\Leftrightarrow &-16x
& = &14\\\Leftrightarrow & \color{red}{-16}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+5}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-x }
& = & -3 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -3 \color{blue}{-5} \\\Leftrightarrow &-7x
& = &-8\\\Leftrightarrow & \color{red}{-7}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+3}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3-13x }
& = & 7 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -4x \color{blue}{-13x }
& = & 7 \color{blue}{-3} \\\Leftrightarrow &-17x
& = &4\\\Leftrightarrow & \color{red}{-17}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-7}& = & -14 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7-8x }
& = & -14 \color{red}{ +8x }\color{blue}{+7-8x } \\\Leftrightarrow & 3x \color{blue}{-8x }
& = & -14 \color{blue}{+7} \\\Leftrightarrow &-5x
& = &-7\\\Leftrightarrow & \color{red}{-5}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)