Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(2x+15=4+x\)
- \(-15x+9=-2+x\)
- \(-2x+4=12+x\)
- \(-10x-4=-2+x\)
- \(-11x+1=-7+6x\)
- \(12x-4=15+x\)
- \(-5x-13=7+x\)
- \(x-8=1-2x\)
- \(14x+4=-10+11x\)
- \(10x+2=-14+13x\)
- \(-14x+11=-15+x\)
- \(13x+11=-13-6x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 2x \color{red}{+15}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x }
& = & 4 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & 4 \color{blue}{-15} \\\Leftrightarrow &x
& = &-11\\\Leftrightarrow & \color{red}{}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+9}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-x }
& = & -2 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & -2 \color{blue}{-9} \\\Leftrightarrow &-16x
& = &-11\\\Leftrightarrow & \color{red}{-16}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{11}{16} } & & \\ & V = \left\{ \frac{11}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+4}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-x }
& = & 12 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & 12 \color{blue}{-4} \\\Leftrightarrow &-3x
& = &8\\\Leftrightarrow & \color{red}{-3}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-4}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x }
& = & -2 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -2 \color{blue}{+4} \\\Leftrightarrow &-11x
& = &2\\\Leftrightarrow & \color{red}{-11}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+1}& = & -7 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-6x }
& = & -7 \color{red}{ +6x }\color{blue}{-1-6x } \\\Leftrightarrow & -11x \color{blue}{-6x }
& = & -7 \color{blue}{-1} \\\Leftrightarrow &-17x
& = &-8\\\Leftrightarrow & \color{red}{-17}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-4}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4-x }
& = & 15 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & 15 \color{blue}{+4} \\\Leftrightarrow &11x
& = &19\\\Leftrightarrow & \color{red}{11}x
& = &19\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{19}{11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-13}\color{blue}{+13-x }
& = & 7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 7 \color{blue}{+13} \\\Leftrightarrow &-6x
& = &20\\\Leftrightarrow & \color{red}{-6}x
& = &20\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{20}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-8}& = & 1 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8+2x }
& = & 1 \color{red}{ -2x }\color{blue}{+8+2x } \\\Leftrightarrow & x \color{blue}{+2x }
& = & 1 \color{blue}{+8} \\\Leftrightarrow &3x
& = &9\\\Leftrightarrow & \color{red}{3}x
& = &9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{9}{3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+4}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4-11x }
& = & -10 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 14x \color{blue}{-11x }
& = & -10 \color{blue}{-4} \\\Leftrightarrow &3x
& = &-14\\\Leftrightarrow & \color{red}{3}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{-14}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+2}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2-13x }
& = & -14 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & 10x \color{blue}{-13x }
& = & -14 \color{blue}{-2} \\\Leftrightarrow &-3x
& = &-16\\\Leftrightarrow & \color{red}{-3}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+11}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-x }
& = & -15 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -15 \color{blue}{-11} \\\Leftrightarrow &-15x
& = &-26\\\Leftrightarrow & \color{red}{-15}x
& = &-26\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-26}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{26}{15} } & & \\ & V = \left\{ \frac{26}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+11}& = & -13 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11+6x }
& = & -13 \color{red}{ -6x }\color{blue}{-11+6x } \\\Leftrightarrow & 13x \color{blue}{+6x }
& = & -13 \color{blue}{-11} \\\Leftrightarrow &19x
& = &-24\\\Leftrightarrow & \color{red}{19}x
& = &-24\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-24}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{19} } & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)