Question

Giải các phương trình sau

Answer 1

Answer 2

1. \(1+\dfrac{2x-5}{6}=\dfrac{3-x}{4}\)

\(\Leftrightarrow\dfrac{4x+2}{12}=\dfrac{9-3x}{12}\)

\(\Leftrightarrow4x+2=9-3x\)

\(\Leftrightarrow7x=7\)

\(\Leftrightarrow x=1\)

Vậy: Phương trình có tập nghiệm \(S=\left\{1\right\}\)

2. \(\dfrac{3x-9}{5}=\dfrac{3-x}{2}\)

\(\Leftrightarrow\dfrac{6x-18}{10}=\dfrac{15-5x}{10}\)

\(\Leftrightarrow6x-18=15-5x\)

\(\Leftrightarrow11x=23\)

\(\Leftrightarrow x=\dfrac{23}{11}\)

Vậy: .....

Answer 3

a) \(1+\dfrac{2x-5}{6}=\dfrac{3-x}{4}\)

\(\Leftrightarrow\dfrac{12}{12}+\dfrac{2.\left(2x-5\right)}{6.2}=\dfrac{3\left(3-x\right)}{4.3}\)

\(\Leftrightarrow12+4x-10-9+3x=0\)

\(\Leftrightarrow7x=7\)

\(\Leftrightarrow x=1\)

b) \(\dfrac{3x-9}{5}=\dfrac{3-x}{2}\)

\(\Leftrightarrow\dfrac{2\left(3x-9\right)}{5.2}=\dfrac{5\left(3-x\right)}{2.5}\)

\(\Leftrightarrow6x-18-15+5x=0\)

\(\Leftrightarrow x=3\)

Answer 4

- Cảm ơn bạn đã đăng bài :)

1)\(1+\dfrac{2x-5}{6}=\dfrac{3-x}{4}\) ⇔\(\dfrac{2x+1}{6}=\dfrac{3-x}{4}\) ⇔\(\dfrac{4x+2}{12}=\dfrac{9-3x}{12}\)

⇔4x+2=9-3x ⇔7x-7=0 ⇔x=1

2)\(\dfrac{3x-9}{3}=\dfrac{3-x}{2}\) ⇔\(x-3=\dfrac{3-x}{2}\) ⇔\(\dfrac{2x-6}{2}=\dfrac{3-x}{2}\)

⇔2x-6=3-x ⇔3x-9=0 ⇔x=3

 

Answer 5

\(1,\Leftrightarrow\dfrac{12+2\left(2x-5\right)}{12}=\dfrac{3\left(3-x\right)}{12}\)

\(\Leftrightarrow12+4x-10-9+3x=0\)

\(\Leftrightarrow7x-7=0\)

\(\Leftrightarrow7x=7\)

\(\Leftrightarrow x=7\)

Vậy \(S=\left\{7\right\}\)

\(2,\Leftrightarrow\dfrac{2\left(3x-9\right)}{10}=\dfrac{5\left(3-x\right)}{10}\)

\(\Leftrightarrow6x-18-15+5x=0\)

\(\Leftrightarrow11x-33=0\)

\(\Leftrightarrow11x=33\)

\(\Leftrightarrow x=3\)

Vậy \(S=\left\{3\right\}\)

Answer 6

1. \(\Leftrightarrow\dfrac{12}{12}+\dfrac{2.\left(2x-5\right)}{12}=\dfrac{3.\left(3-x\right)}{12}\\ \Leftrightarrow12+4x-10=9-3x\\ \Leftrightarrow4x+3x=9-12+10\\ \Leftrightarrow7x=5\\ \Leftrightarrow x=\dfrac{5}{7}\)

Vậy x có tập nghiệm là \(\dfrac{5}{7}\)

2.

\(\Leftrightarrow\dfrac{2\left(3x-9\right)}{10}=\dfrac{5\left(3-x\right)}{10}\\ \Leftrightarrow6x-18=15-5x\\ \Leftrightarrow6x+5x=15+18\\ \Leftrightarrow11x=33\\ \Leftrightarrow x=\dfrac{33}{11}=3\)

Vậy x có tập nghiệm là 3