Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(10x-15=-6+x\)
- \(-2x+10=-8+x\)
- \(9x-1=12+2x\)
- \(-4x+3=-11+x\)
- \(-11x-15=11+x\)
- \(-3x-6=2+x\)
- \(14x+1=-3-13x\)
- \(-15x-10=1+13x\)
- \(-13x-3=12+x\)
- \(6x+12=-8-5x\)
- \(-5x+3=-3+11x\)
- \(-7x+15=4+11x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 10x \color{red}{-15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15-x }
& = & -6 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 10x \color{blue}{-x }
& = & -6 \color{blue}{+15} \\\Leftrightarrow &9x
& = &9\\\Leftrightarrow & \color{red}{9}x
& = &9\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{9}{9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+10}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-x }
& = & -8 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & -8 \color{blue}{-10} \\\Leftrightarrow &-3x
& = &-18\\\Leftrightarrow & \color{red}{-3}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-18}{-3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-1}& = & 12 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1-2x }
& = & 12 \color{red}{ +2x }\color{blue}{+1-2x } \\\Leftrightarrow & 9x \color{blue}{-2x }
& = & 12 \color{blue}{+1} \\\Leftrightarrow &7x
& = &13\\\Leftrightarrow & \color{red}{7}x
& = &13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3-x }
& = & -11 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -11 \color{blue}{-3} \\\Leftrightarrow &-5x
& = &-14\\\Leftrightarrow & \color{red}{-5}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-15}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x }
& = & 11 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 11 \color{blue}{+15} \\\Leftrightarrow &-12x
& = &26\\\Leftrightarrow & \color{red}{-12}x
& = &26\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{26}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-6}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x }
& = & 2 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 2 \color{blue}{+6} \\\Leftrightarrow &-4x
& = &8\\\Leftrightarrow & \color{red}{-4}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+1}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1+13x }
& = & -3 \color{red}{ -13x }\color{blue}{-1+13x } \\\Leftrightarrow & 14x \color{blue}{+13x }
& = & -3 \color{blue}{-1} \\\Leftrightarrow &27x
& = &-4\\\Leftrightarrow & \color{red}{27}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}}
& = & \frac{-4}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{27} } & & \\ & V = \left\{ \frac{-4}{27} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-10}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-13x }
& = & 1 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & 1 \color{blue}{+10} \\\Leftrightarrow &-28x
& = &11\\\Leftrightarrow & \color{red}{-28}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{11}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{28} } & & \\ & V = \left\{ \frac{-11}{28} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-3}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-x }
& = & 12 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 12 \color{blue}{+3} \\\Leftrightarrow &-14x
& = &15\\\Leftrightarrow & \color{red}{-14}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{14} } & & \\ & V = \left\{ \frac{-15}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+12}& = & -8 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12+5x }
& = & -8 \color{red}{ -5x }\color{blue}{-12+5x } \\\Leftrightarrow & 6x \color{blue}{+5x }
& = & -8 \color{blue}{-12} \\\Leftrightarrow &11x
& = &-20\\\Leftrightarrow & \color{red}{11}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+3}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-11x }
& = & -3 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & -5x \color{blue}{-11x }
& = & -3 \color{blue}{-3} \\\Leftrightarrow &-16x
& = &-6\\\Leftrightarrow & \color{red}{-16}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+15}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-11x }
& = & 4 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & -7x \color{blue}{-11x }
& = & 4 \color{blue}{-15} \\\Leftrightarrow &-18x
& = &-11\\\Leftrightarrow & \color{red}{-18}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}}
& = & \frac{-11}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{11}{18} } & & \\ & V = \left\{ \frac{11}{18} \right\} & \\\end{align}\)