Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-13x-1=-10+x\)
- \(14x+8=12+x\)
- \(-7x+1=13+x\)
- \(-4x+2=13+9x\)
- \(-14x-15=14+x\)
- \(8x+6=14-13x\)
- \(3x-13=-8+8x\)
- \(-4x-5=10+13x\)
- \(13x+7=-6-2x\)
- \(-14x-9=12+x\)
- \(-3x-8=1+x\)
- \(-9x+12=14+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -13x \color{red}{-1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-x }
& = & -10 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -10 \color{blue}{+1} \\\Leftrightarrow &-14x
& = &-9\\\Leftrightarrow & \color{red}{-14}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+8}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8-x }
& = & 12 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & 12 \color{blue}{-8} \\\Leftrightarrow &13x
& = &4\\\Leftrightarrow & \color{red}{13}x
& = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+1}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x }
& = & 13 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & 13 \color{blue}{-1} \\\Leftrightarrow &-8x
& = &12\\\Leftrightarrow & \color{red}{-8}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+2}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2-9x }
& = & 13 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & -4x \color{blue}{-9x }
& = & 13 \color{blue}{-2} \\\Leftrightarrow &-13x
& = &11\\\Leftrightarrow & \color{red}{-13}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-15}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-15}\color{blue}{+15-x }
& = & 14 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 14 \color{blue}{+15} \\\Leftrightarrow &-15x
& = &29\\\Leftrightarrow & \color{red}{-15}x
& = &29\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{29}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{15} } & & \\ & V = \left\{ \frac{-29}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+6}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6+13x }
& = & 14 \color{red}{ -13x }\color{blue}{-6+13x } \\\Leftrightarrow & 8x \color{blue}{+13x }
& = & 14 \color{blue}{-6} \\\Leftrightarrow &21x
& = &8\\\Leftrightarrow & \color{red}{21}x
& = &8\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}}
& = & \frac{8}{21} \\\Leftrightarrow & \color{green}{ x = \frac{8}{21} } & & \\ & V = \left\{ \frac{8}{21} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-13}& = & -8 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13-8x }
& = & -8 \color{red}{ +8x }\color{blue}{+13-8x } \\\Leftrightarrow & 3x \color{blue}{-8x }
& = & -8 \color{blue}{+13} \\\Leftrightarrow &-5x
& = &5\\\Leftrightarrow & \color{red}{-5}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-5}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-13x }
& = & 10 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -4x \color{blue}{-13x }
& = & 10 \color{blue}{+5} \\\Leftrightarrow &-17x
& = &15\\\Leftrightarrow & \color{red}{-17}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{15}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{17} } & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+7}& = & -6 \color{red}{ -2x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7+2x }
& = & -6 \color{red}{ -2x }\color{blue}{-7+2x } \\\Leftrightarrow & 13x \color{blue}{+2x }
& = & -6 \color{blue}{-7} \\\Leftrightarrow &15x
& = &-13\\\Leftrightarrow & \color{red}{15}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{-13}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-9}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-x }
& = & 12 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 12 \color{blue}{+9} \\\Leftrightarrow &-15x
& = &21\\\Leftrightarrow & \color{red}{-15}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{21}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8-x }
& = & 1 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 1 \color{blue}{+8} \\\Leftrightarrow &-4x
& = &9\\\Leftrightarrow & \color{red}{-4}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+12}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12-x }
& = & 14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 14 \color{blue}{-12} \\\Leftrightarrow &-10x
& = &2\\\Leftrightarrow & \color{red}{-10}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)