Solve 1/3(3/5*a+1)=13/5

$$\frac { 1 } { 3 } ( \frac { 3 } { 5 } \cdot a + 1 ) = \frac { 13 } { 5 }$$

Solve for a

$$a = \frac{34}{3} = 11\frac{1}{3} \approx 11.333333333$$

Steps for Solving Linear Equation

Multiply both sides by 3, the reciprocal of \frac{1}{3}.

$$\frac{3}{5}a+1=\frac{13}{5}\times 3$$

Express \frac{13}{5}\times 3 as a single fraction.

$$\frac{3}{5}a+1=\frac{13\times 3}{5}$$

Multiply 13 and 3 to get 39.

$$\frac{3}{5}a+1=\frac{39}{5}$$

Subtract 1 from both sides.

$$\frac{3}{5}a=\frac{39}{5}-1$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{3}{5}a=\frac{39}{5}-\frac{5}{5}$$

Since \frac{39}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{5}a=\frac{39-5}{5}$$

Subtract 5 from 39 to get 34.

$$\frac{3}{5}a=\frac{34}{5}$$

Multiply both sides by \frac{5}{3}, the reciprocal of \frac{3}{5}.

$$a=\frac{34}{5}\times \frac{5}{3}$$

Multiply \frac{34}{5} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{34\times 5}{5\times 3}$$

Cancel out 5 in both numerator and denominator.

$$a=\frac{34}{3}$$