Solve 15.3>3(a-1.4)

$$15.3 > 3 ( a - 1.4 )$$

Solve for a

$$a<\frac{13}{2}$$

Solution Steps

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$\frac{15.3}{3}>a-1.4$$

Expand \frac{15.3}{3} by multiplying both numerator and the denominator by 10.

$$\frac{153}{30}>a-1.4$$

Reduce the fraction \frac{153}{30} to lowest terms by extracting and canceling out 3.

$$\frac{51}{10}>a-1.4$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$a-1.4<\frac{51}{10}$$

Add 1.4 to both sides.

$$a<\frac{51}{10}+1.4$$

Convert decimal number 1.4 to fraction \frac{14}{10}. Reduce the fraction \frac{14}{10} to lowest terms by extracting and canceling out 2.

$$a<\frac{51}{10}+\frac{7}{5}$$

Least common multiple of 10 and 5 is 10. Convert \frac{51}{10} and \frac{7}{5} to fractions with denominator 10.

$$a<\frac{51}{10}+\frac{14}{10}$$

Since \frac{51}{10} and \frac{14}{10} have the same denominator, add them by adding their numerators.

$$a<\frac{51+14}{10}$$

Add 51 and 14 to get 65.

$$a<\frac{65}{10}$$

Reduce the fraction \frac{65}{10} to lowest terms by extracting and canceling out 5.

$$a<\frac{13}{2}$$