1a/ \(7x+9=30\)
\(\Leftrightarrow7x=21\)
\(\Leftrightarrow x=3\)
Vậy S=\(\left\{3\right\}\)
b/ \(3\left(x-1\right)-2=4\)
\(\Leftrightarrow3x-3-2=4\)
\(\Leftrightarrow3x=9\)
\(\Leftrightarrow x=3\)
Vậy S=\(\left\{3\right\}\)
c/ \(\dfrac{x+2}{4}=\dfrac{x-1}{6}+\dfrac{3-x}{3}\)
\(\Leftrightarrow\dfrac{3\left(x+2\right)}{12}=\dfrac{2\left(x-1\right)}{12}+\dfrac{4\left(3-x\right)}{3}\)
\(\Rightarrow3x+6=2x-2+12-4x\)
\(\Leftrightarrow3x-2x+4x=-2+12-6\)
\(\Leftrightarrow5x=4\)
\(\Leftrightarrow x=\dfrac{4}{5}\)
Vậy S= \(\left\{\dfrac{4}{5}\right\}\)
d/\(\dfrac{x+1}{x}-\dfrac{3x}{x\left(x+4\right)}=\dfrac{x-2}{x+4}\) ĐKXĐ: \(x\ne0;x\ne-4\)
\(\Leftrightarrow\dfrac{\left(x+1\right)\left(x+4\right)}{x\left(x+4\right)}-\dfrac{3x}{x\left(x+4\right)}=\dfrac{x\left(x-2\right)}{x\left(x+4\right)}\)
\(\Rightarrow x^2+4x+x+4-3x=x^2-2x\)
\(\Leftrightarrow x^2+4x+x-3x-x^2+2x=-4\)
\(\Leftrightarrow4x=-4\)
\(\Leftrightarrow x=-1\left(nhận\right)\)
Vậy S=\(\left\{-1\right\}\)
\(a)7x+9=30\)
\(\Leftrightarrow7x=21\)
\(\Leftrightarrow x=3\)
\(\text{Vậy phương trình có tập nghiệm là }S=\left\{3\right\}\)
\(b)3\left(x-1\right)-2=4\)
\(\Leftrightarrow3x-3-2=4\)
\(\Leftrightarrow3x-5=4\)
\(\Leftrightarrow3x=9\)
\(\Leftrightarrow x=3\)
\(\text{Vậy phương trình có tập nghiệm là }S=\left\{3\right\}\)
\(c)\dfrac{x+2}{4}=\dfrac{x-1}{6}+\dfrac{3-x}{3}\)
\(\Leftrightarrow\dfrac{3\left(x+2\right)}{12}=\dfrac{2\left(x-1\right)}{12}+\dfrac{4\left(3-x\right)}{12}\)
\(\Leftrightarrow3x+6=2x-2+12-4x\)
\(\Leftrightarrow3x+6=10-2x\)
\(\Leftrightarrow3x+6-10+2x=0\)
\(\Leftrightarrow5x-4=0\)
\(\Leftrightarrow5x=4\)
\(\Leftrightarrow x=\dfrac{4}{5}\)
\(\text{Vậy phương trình có tập nghiệm là }S=\left\{\dfrac{4}{5}\right\}\)
\(d)\dfrac{x+1}{x}-\dfrac{3x}{x\left(x+4\right)}=\dfrac{x-2}{x+4}\text{ĐKXĐ:}x\ne0;x\ne-4\)
\(\Leftrightarrow\dfrac{\left(x+1\right)\left(x+4\right)}{x\left(x+4\right)}-\dfrac{3x}{x\left(x+4\right)}=\dfrac{x\left(x-2\right)}{x\left(x+4\right)}\)
\(\Rightarrow x^2+4x+x+4-3x=x^2-2x\)
\(\Leftrightarrow x^2+2x+4=x^2-2x\)
\(\Leftrightarrow x^2+2x+4-x^2+2x=0\)
\(\Leftrightarrow4x+4=0\)
\(\Leftrightarrow4x=-4\)
\(\Leftrightarrow x=-1\left(TM\text{Đ}KX\text{Đ}\right)\)
\(\text{Vậy phương trình có tập nghiệm là }S=\left\{-1\right\}\)
