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