Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(8x+2=9+x\)
- \(14x+5=15-11x\)
- \(9x-4=-2+13x\)
- \(-12x+6=8+5x\)
- \(-14x-1=-9+5x\)
- \(-3x-9=-9+x\)
- \(10x-10=7-3x\)
- \(4x+8=-6+7x\)
- \(-9x-4=-13+x\)
- \(-9x+6=1+x\)
- \(10x+12=9-9x\)
- \(x-6=6-12x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 8x \color{red}{+2}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+2}\color{blue}{-2-x }
& = & 9 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 8x \color{blue}{-x }
& = & 9 \color{blue}{-2} \\\Leftrightarrow &7x
& = &7\\\Leftrightarrow & \color{red}{7}x
& = &7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{7}{7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+5}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5+11x }
& = & 15 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 14x \color{blue}{+11x }
& = & 15 \color{blue}{-5} \\\Leftrightarrow &25x
& = &10\\\Leftrightarrow & \color{red}{25}x
& = &10\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{10}{25} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-4}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4-13x }
& = & -2 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & 9x \color{blue}{-13x }
& = & -2 \color{blue}{+4} \\\Leftrightarrow &-4x
& = &2\\\Leftrightarrow & \color{red}{-4}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+6}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-5x }
& = & 8 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & -12x \color{blue}{-5x }
& = & 8 \color{blue}{-6} \\\Leftrightarrow &-17x
& = &2\\\Leftrightarrow & \color{red}{-17}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-1}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-5x }
& = & -9 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & -14x \color{blue}{-5x }
& = & -9 \color{blue}{+1} \\\Leftrightarrow &-19x
& = &-8\\\Leftrightarrow & \color{red}{-19}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-8}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{8}{19} } & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-x }
& = & -9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -9 \color{blue}{+9} \\\Leftrightarrow &-4x
& = &0\\\Leftrightarrow & \color{red}{-4}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-10}& = & 7 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10+3x }
& = & 7 \color{red}{ -3x }\color{blue}{+10+3x } \\\Leftrightarrow & 10x \color{blue}{+3x }
& = & 7 \color{blue}{+10} \\\Leftrightarrow &13x
& = &17\\\Leftrightarrow & \color{red}{13}x
& = &17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+8}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8-7x }
& = & -6 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & 4x \color{blue}{-7x }
& = & -6 \color{blue}{-8} \\\Leftrightarrow &-3x
& = &-14\\\Leftrightarrow & \color{red}{-3}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-4}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-4}\color{blue}{+4-x }
& = & -13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -13 \color{blue}{+4} \\\Leftrightarrow &-10x
& = &-9\\\Leftrightarrow & \color{red}{-10}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+6}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-x }
& = & 1 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 1 \color{blue}{-6} \\\Leftrightarrow &-10x
& = &-5\\\Leftrightarrow & \color{red}{-10}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+12}& = & 9 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12+9x }
& = & 9 \color{red}{ -9x }\color{blue}{-12+9x } \\\Leftrightarrow & 10x \color{blue}{+9x }
& = & 9 \color{blue}{-12} \\\Leftrightarrow &19x
& = &-3\\\Leftrightarrow & \color{red}{19}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-6}& = & 6 \color{red}{ -12x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6+12x }
& = & 6 \color{red}{ -12x }\color{blue}{+6+12x } \\\Leftrightarrow & x \color{blue}{+12x }
& = & 6 \color{blue}{+6} \\\Leftrightarrow &13x
& = &12\\\Leftrightarrow & \color{red}{13}x
& = &12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)