Solve {l}{9n+6*7=1.1{(3n+1/2)}}{o=46}{text{Solvefor}ptext{where}}{p=o}

$$\left. \begin{array} { l } { 9 n + 6 \cdot 7 = 1.1 {(\frac{3 n + 1}{2})} }\\ { o = 46 }\\ { \text{Solve for } p \text{ where} } \\ { p = o } \end{array} \right.$$

Solve for n, o, p

$$p=46$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 2.

$$18n+12\times 7=1.1\left(3n+1\right)$$

Multiply 12 and 7 to get 84.

$$18n+84=1.1\left(3n+1\right)$$

Use the distributive property to multiply 1.1 by 3n+1.

$$18n+84=3.3n+1.1$$

Subtract 3.3n from both sides.

$$18n+84-3.3n=1.1$$

Combine 18n and -3.3n to get 14.7n.

$$14.7n+84=1.1$$

Subtract 84 from both sides.

$$14.7n=1.1-84$$

Subtract 84 from 1.1 to get -82.9.

$$14.7n=-82.9$$

Divide both sides by 14.7.

$$n=\frac{-82.9}{14.7}$$

Expand \frac{-82.9}{14.7} by multiplying both numerator and the denominator by 10.

$$n=\frac{-829}{147}$$

Fraction \frac{-829}{147} can be rewritten as -\frac{829}{147} by extracting the negative sign.

$$n=-\frac{829}{147}$$

The system is now solved.

$$n=-\frac{829}{147} o=46 p=46$$