Solve 45(2n-1)=31(5n+4)

$$45 ( 2 n - 1 ) = 31 ( 5 n + 4 )$$

Solve for n

$$n = -\frac{13}{5} = -2\frac{3}{5} = -2.6$$

Steps for Solving Linear Equation

Use the distributive property to multiply 45 by 2n-1.

$$90n-45=31\left(5n+4\right)$$

Use the distributive property to multiply 31 by 5n+4.

$$90n-45=155n+124$$

Subtract 155n from both sides.

$$90n-45-155n=124$$

Combine 90n and -155n to get -65n.

$$-65n-45=124$$

Add 45 to both sides.

$$-65n=124+45$$

Add 124 and 45 to get 169.

$$-65n=169$$

Divide both sides by -65.

$$n=\frac{169}{-65}$$

Reduce the fraction \frac{169}{-65} to lowest terms by extracting and canceling out 13.

$$n=-\frac{13}{5}$$