Solve 2/7+3/5=x*3+1/2

$$\frac{ 2 }{ 7 } + \frac{ 3 }{ 5 } =x \times 3+ \frac{ 1 }{ 2 }$$

Solve for x

$$x=\frac{9}{70}\approx 0.128571429$$

Steps for Solving Linear Equation

Least common multiple of 7 and 5 is 35. Convert \frac{2}{7} and \frac{3}{5} to fractions with denominator 35.

$$\frac{10}{35}+\frac{21}{35}=x\times 3+\frac{1}{2}$$

Since \frac{10}{35} and \frac{21}{35} have the same denominator, add them by adding their numerators.

$$\frac{10+21}{35}=x\times 3+\frac{1}{2}$$

Add 10 and 21 to get 31.

$$\frac{31}{35}=x\times 3+\frac{1}{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x\times 3+\frac{1}{2}=\frac{31}{35}$$

Subtract \frac{1}{2} from both sides.

$$x\times 3=\frac{31}{35}-\frac{1}{2}$$

Least common multiple of 35 and 2 is 70. Convert \frac{31}{35} and \frac{1}{2} to fractions with denominator 70.

$$x\times 3=\frac{62}{70}-\frac{35}{70}$$

Since \frac{62}{70} and \frac{35}{70} have the same denominator, subtract them by subtracting their numerators.

$$x\times 3=\frac{62-35}{70}$$

Subtract 35 from 62 to get 27.

$$x\times 3=\frac{27}{70}$$

Divide both sides by 3.

$$x=\frac{\frac{27}{70}}{3}$$

Express \frac{\frac{27}{70}}{3} as a single fraction.

$$x=\frac{27}{70\times 3}$$

Multiply 70 and 3 to get 210.

$$x=\frac{27}{210}$$

Reduce the fraction \frac{27}{210} to lowest terms by extracting and canceling out 3.

$$x=\frac{9}{70}$$