Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-7x+1=14+x\)
- \(9x+11=-10-13x\)
- \(-7x-15=11+4x\)
- \(-15x-1=-2+13x\)
- \(-2x+7=-6+11x\)
- \(-5x+13=12+3x\)
- \(-7x+5=14+x\)
- \(7x+8=8-3x\)
- \(-3x-7=-11+x\)
- \(-7x-15=6+11x\)
- \(4x-2=-12+13x\)
- \(-10x-12=-9+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -7x \color{red}{+1}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x }
& = & 14 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & 14 \color{blue}{-1} \\\Leftrightarrow &-8x
& = &13\\\Leftrightarrow & \color{red}{-8}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+11}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+11}\color{blue}{-11+13x }
& = & -10 \color{red}{ -13x }\color{blue}{-11+13x } \\\Leftrightarrow & 9x \color{blue}{+13x }
& = & -10 \color{blue}{-11} \\\Leftrightarrow &22x
& = &-21\\\Leftrightarrow & \color{red}{22}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}}
& = & \frac{-21}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{22} } & & \\ & V = \left\{ \frac{-21}{22} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-15}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-4x }
& = & 11 \color{red}{ +4x }\color{blue}{+15-4x } \\\Leftrightarrow & -7x \color{blue}{-4x }
& = & 11 \color{blue}{+15} \\\Leftrightarrow &-11x
& = &26\\\Leftrightarrow & \color{red}{-11}x
& = &26\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{26}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{11} } & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-1}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-13x }
& = & -2 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & -2 \color{blue}{+1} \\\Leftrightarrow &-28x
& = &-1\\\Leftrightarrow & \color{red}{-28}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{-1}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{1}{28} } & & \\ & V = \left\{ \frac{1}{28} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+7}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{+7}\color{blue}{-7-11x }
& = & -6 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & -2x \color{blue}{-11x }
& = & -6 \color{blue}{-7} \\\Leftrightarrow &-13x
& = &-13\\\Leftrightarrow & \color{red}{-13}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+13}& = & 12 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-3x }
& = & 12 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & -5x \color{blue}{-3x }
& = & 12 \color{blue}{-13} \\\Leftrightarrow &-8x
& = &-1\\\Leftrightarrow & \color{red}{-8}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+5}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-x }
& = & 14 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & 14 \color{blue}{-5} \\\Leftrightarrow &-8x
& = &9\\\Leftrightarrow & \color{red}{-8}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+8}& = & 8 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8+3x }
& = & 8 \color{red}{ -3x }\color{blue}{-8+3x } \\\Leftrightarrow & 7x \color{blue}{+3x }
& = & 8 \color{blue}{-8} \\\Leftrightarrow &10x
& = &0\\\Leftrightarrow & \color{red}{10}x
& = &0\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{0}{10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-7}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-x }
& = & -11 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -11 \color{blue}{+7} \\\Leftrightarrow &-4x
& = &-4\\\Leftrightarrow & \color{red}{-4}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-15}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-11x }
& = & 6 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & -7x \color{blue}{-11x }
& = & 6 \color{blue}{+15} \\\Leftrightarrow &-18x
& = &21\\\Leftrightarrow & \color{red}{-18}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}}
& = & \frac{21}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-2}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2-13x }
& = & -12 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & 4x \color{blue}{-13x }
& = & -12 \color{blue}{+2} \\\Leftrightarrow &-9x
& = &-10\\\Leftrightarrow & \color{red}{-9}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-12}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12-x }
& = & -9 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -9 \color{blue}{+12} \\\Leftrightarrow &-11x
& = &3\\\Leftrightarrow & \color{red}{-11}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)