Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-15x+9=1+13x\)
- \(-x-7=5+3x\)
- \(-12x-7=3+13x\)
- \(-9x+15=-11+x\)
- \(11x-10=13+7x\)
- \(5x-15=-2+3x\)
- \(-9x+9=3+x\)
- \(-13x-7=-2+7x\)
- \(-13x+5=-13+7x\)
- \(-12x-9=-7+x\)
- \(-13x+6=10+x\)
- \(-x-11=9-7x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -15x \color{red}{+9}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-13x }
& = & 1 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & 1 \color{blue}{-9} \\\Leftrightarrow &-28x
& = &-8\\\Leftrightarrow & \color{red}{-28}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{-8}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-7}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7-3x }
& = & 5 \color{red}{ +3x }\color{blue}{+7-3x } \\\Leftrightarrow & -x \color{blue}{-3x }
& = & 5 \color{blue}{+7} \\\Leftrightarrow &-4x
& = &12\\\Leftrightarrow & \color{red}{-4}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-7}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-13x }
& = & 3 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & 3 \color{blue}{+7} \\\Leftrightarrow &-25x
& = &10\\\Leftrightarrow & \color{red}{-25}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{10}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-x }
& = & -11 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -11 \color{blue}{-15} \\\Leftrightarrow &-10x
& = &-26\\\Leftrightarrow & \color{red}{-10}x
& = &-26\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-26}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-10}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10-7x }
& = & 13 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & 11x \color{blue}{-7x }
& = & 13 \color{blue}{+10} \\\Leftrightarrow &4x
& = &23\\\Leftrightarrow & \color{red}{4}x
& = &23\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{23}{4} \\\Leftrightarrow & \color{green}{ x = \frac{23}{4} } & & \\ & V = \left\{ \frac{23}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-15}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{-15}\color{blue}{+15-3x }
& = & -2 \color{red}{ +3x }\color{blue}{+15-3x } \\\Leftrightarrow & 5x \color{blue}{-3x }
& = & -2 \color{blue}{+15} \\\Leftrightarrow &2x
& = &13\\\Leftrightarrow & \color{red}{2}x
& = &13\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{13}{2} \\\Leftrightarrow & \color{green}{ x = \frac{13}{2} } & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+9}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-x }
& = & 3 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 3 \color{blue}{-9} \\\Leftrightarrow &-10x
& = &-6\\\Leftrightarrow & \color{red}{-10}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-7}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-7x }
& = & -2 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -13x \color{blue}{-7x }
& = & -2 \color{blue}{+7} \\\Leftrightarrow &-20x
& = &5\\\Leftrightarrow & \color{red}{-20}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{5}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+5}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5-7x }
& = & -13 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -13x \color{blue}{-7x }
& = & -13 \color{blue}{-5} \\\Leftrightarrow &-20x
& = &-18\\\Leftrightarrow & \color{red}{-20}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{-18}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-9}\color{blue}{+9-x }
& = & -7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -7 \color{blue}{+9} \\\Leftrightarrow &-13x
& = &2\\\Leftrightarrow & \color{red}{-13}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-x }
& = & 10 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 10 \color{blue}{-6} \\\Leftrightarrow &-14x
& = &4\\\Leftrightarrow & \color{red}{-14}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-11}& = & 9 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11+7x }
& = & 9 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & -x \color{blue}{+7x }
& = & 9 \color{blue}{+11} \\\Leftrightarrow &6x
& = &20\\\Leftrightarrow & \color{red}{6}x
& = &20\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}}
& = & \frac{20}{6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)