Solve S=38000N/76frac{N{mm^2}}

$$S = \frac { 38000 N } { 76 \frac { N } { m m ^ { 2 } } }$$

Solve for N

$$N\neq 0$$

$$S=500m^{3}\text{ and }m\neq 0\text{ and }N\neq 0$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$S=\frac{38000N}{76\times \frac{N}{m^{3}}}$$

Express 76\times \frac{N}{m^{3}} as a single fraction.

$$S=\frac{38000N}{\frac{76N}{m^{3}}}$$

Divide 38000N by \frac{76N}{m^{3}} by multiplying 38000N by the reciprocal of \frac{76N}{m^{3}}.

$$S=\frac{38000Nm^{3}}{76N}$$

Cancel out 76 in both numerator and denominator.

$$S=\frac{500Nm^{3}}{N}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{500Nm^{3}}{N}=S$$

Variable N cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by N.

$$500Nm^{3}=SN$$

Subtract SN from both sides.

$$500Nm^{3}-SN=0$$

Combine all terms containing N.

$$\left(500m^{3}-S\right)N=0$$

Divide 0 by 500m^{3}-S.

$$N=0$$

Variable N cannot be equal to 0.

$$N\in \emptyset$$

Solve for S

$$S=500m^{3}$$

$$N\neq 0\text{ and }m\neq 0$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$S=\frac{38000N}{76\times \frac{N}{m^{3}}}$$

Express 76\times \frac{N}{m^{3}} as a single fraction.

$$S=\frac{38000N}{\frac{76N}{m^{3}}}$$

Divide 38000N by \frac{76N}{m^{3}} by multiplying 38000N by the reciprocal of \frac{76N}{m^{3}}.

$$S=\frac{38000Nm^{3}}{76N}$$

Cancel out 76N in both numerator and denominator.

$$S=500m^{3}$$