Solve 7a/5>4a/2+3/10

$$\frac { 7 a } { 5 } > \frac { 4 a } { 2 } + \frac { 3 } { 10 }$$

Solve for a

$$a<-\frac{1}{2}$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 5,2,10. Since 10 is positive, the inequality direction remains the same.

$$2\times 7a>5\times 4a+3$$

Multiply 2 and 7 to get 14.

$$14a>5\times 4a+3$$

Multiply 5 and 4 to get 20.

$$14a>20a+3$$

Subtract 20a from both sides.

$$14a-20a>3$$

Combine 14a and -20a to get -6a.

$$-6a>3$$

Divide both sides by -6. Since -6 is negative, the inequality direction is changed.

$$a<\frac{3}{-6}$$

Reduce the fraction \frac{3}{-6} to lowest terms by extracting and canceling out 3.

$$a<-\frac{1}{2}$$