Solve 4n+3/9+27/5=3n+2/15

$$\frac { 4 n + 3 } { 9 } + \frac { 27 } { 5 } = \frac { 3 n + 2 } { 15 }$$

Solve for n

$$n = -\frac{252}{11} = -22\frac{10}{11} \approx -22.909090909$$

Steps for Solving Linear Equation

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

$$5\left(4n+3\right)+243=3\left(3n+2\right)$$

Use the distributive property to multiply 5 by 4n+3.

$$20n+15+243=3\left(3n+2\right)$$

Add 15 and 243 to get 258.

$$20n+258=3\left(3n+2\right)$$

Use the distributive property to multiply 3 by 3n+2.

$$20n+258=9n+6$$

Subtract 9n from both sides.

$$20n+258-9n=6$$

Combine 20n and -9n to get 11n.

$$11n+258=6$$

Subtract 258 from both sides.

$$11n=6-258$$

Subtract 258 from 6 to get -252.

$$11n=-252$$

Divide both sides by 11.

$$n=\frac{-252}{11}$$

Fraction \frac{-252}{11} can be rewritten as -\frac{252}{11} by extracting the negative sign.

$$n=-\frac{252}{11}$$