Solve a/5+4/15a-6/45a=2a+1/9

$$\frac { a } { 5 } + \frac { 4 } { 15 } a - \frac { 6 } { 45 } a = \frac { 2 a + 1 } { 9 }$$

Solve for a

$$a=1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 45, the least common multiple of 5,15,45,9.

$$45\left(\frac{a}{5}+\frac{4}{15}a\right)-6a=5\left(2a+1\right)$$

Combine \frac{a}{5} and \frac{4}{15}a to get \frac{7}{15}a.

$$45\times \frac{7}{15}a-6a=5\left(2a+1\right)$$

Express 45\times \frac{7}{15} as a single fraction.

$$\frac{45\times 7}{15}a-6a=5\left(2a+1\right)$$

Multiply 45 and 7 to get 315.

$$\frac{315}{15}a-6a=5\left(2a+1\right)$$

Divide 315 by 15 to get 21.

$$21a-6a=5\left(2a+1\right)$$

Combine 21a and -6a to get 15a.

$$15a=5\left(2a+1\right)$$

Use the distributive property to multiply 5 by 2a+1.

$$15a=10a+5$$

Subtract 10a from both sides.

$$15a-10a=5$$

Combine 15a and -10a to get 5a.

$$5a=5$$

Divide both sides by 5.

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

Divide 5 by 5 to get 1.

$$a=1$$