Solve h_{4}=((2kg/s)(2875.3kJ/kg)+(1.2kg/s)(397.96kJ/kg))/4kg/s

$$h _ { 4 } = \frac { ( ( 2 kg / s ) ( 2875.3 kJ / kg ) + ( 1.2 kg / s ) ( 397.96 kJ / kg ) ) } { 4 kg / s }$$

Solve for J

$$J=\frac{500h_{4}}{778519g}$$

$$s\neq 0\text{ and }k\neq 0\text{ and }g\neq 0$$

Steps for Solving Linear Equation

Cancel out k in both numerator and denominator.

$$h_{4}=\frac{\frac{2kg}{s}\times 2875.3Jg+\frac{1.2kg}{s}\times \frac{397.96kJ}{k}g}{\frac{4kg}{s}}$$

Express \frac{2kg}{s}J as a single fraction.

$$h_{4}=\frac{\frac{2kgJ}{s}\times 2875.3g+\frac{1.2kg}{s}\times \frac{397.96kJ}{k}g}{\frac{4kg}{s}}$$

Express \frac{2kgJ}{s}g as a single fraction.

$$h_{4}=\frac{\frac{2kgJg}{s}\times 2875.3+\frac{1.2kg}{s}\times \frac{397.96kJ}{k}g}{\frac{4kg}{s}}$$

Cancel out k in both numerator and denominator.

$$h_{4}=\frac{\frac{2kgJg}{s}\times 2875.3+\frac{1.2kg}{s}\times 397.96Jg}{\frac{4kg}{s}}$$

Multiply g and g to get g^{2}.

$$h_{4}=\frac{\frac{2kg^{2}J}{s}\times 2875.3+\frac{1.2kg}{s}\times 397.96Jg}{\frac{4kg}{s}}$$

Divide \frac{2kg^{2}J}{s}\times 2875.3+\frac{1.2kg}{s}\times 397.96Jg by \frac{4kg}{s} by multiplying \frac{2kg^{2}J}{s}\times 2875.3+\frac{1.2kg}{s}\times 397.96Jg by the reciprocal of \frac{4kg}{s}.

$$h_{4}=\frac{\left(\frac{2kg^{2}J}{s}\times 2875.3+\frac{1.2kg}{s}\times 397.96Jg\right)s}{4kg}$$

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

$$\frac{\left(\frac{2kg^{2}J}{s}\times 2875.3+\frac{1.2kg}{s}\times 397.96Jg\right)s}{4kg}=h_{4}$$

Use the distributive property to multiply \frac{2kg^{2}J}{s}\times 2875.3+\frac{1.2kg}{s}\times 397.96Jg by s.

$$\frac{2875.3\times \frac{2kg^{2}J}{s}s+397.96\times \frac{1.2kg}{s}Jgs}{4kg}=h_{4}$$

Express \frac{2kg^{2}J}{s}s as a single fraction.

$$\frac{2875.3\times \frac{2kg^{2}Js}{s}+397.96\times \frac{1.2kg}{s}Jgs}{4kg}=h_{4}$$

Cancel out s in both numerator and denominator.

$$\frac{2875.3\times 2Jkg^{2}+397.96\times \frac{1.2kg}{s}Jgs}{4kg}=h_{4}$$

Multiply 2875.3 and 2 to get 5750.6.

$$\frac{5750.6Jkg^{2}+397.96\times \frac{1.2kg}{s}Jgs}{4kg}=h_{4}$$

Multiply both sides of the equation by 4gk.

$$5750.6Jkg^{2}+397.96\times \frac{1.2kg}{s}Jgs=h_{4}\times 4gk$$

Reorder the terms.

$$397.96Jgs\times \frac{1.2gk}{s}+5750.6Jkg^{2}=4gh_{4}k$$

Multiply both sides of the equation by s.

$$397.96Jgs\times 1.2gk+5750.6Jkg^{2}s=4gh_{4}ks$$

Multiply 397.96 and 1.2 to get 477.552.

$$477.552Jgsgk+5750.6Jkg^{2}s=4gh_{4}ks$$

Multiply g and g to get g^{2}.

$$477.552Jg^{2}sk+5750.6Jkg^{2}s=4gh_{4}ks$$

Combine 477.552Jg^{2}sk and 5750.6Jkg^{2}s to get 6228.152Jg^{2}sk.

$$6228.152Jg^{2}sk=4gh_{4}ks$$

The equation is in standard form.

$$\frac{778519ksg^{2}}{125}J=4gh_{4}ks$$

Divide both sides by 6228.152g^{2}sk.

$$\frac{125\times \frac{778519ksg^{2}}{125}J}{778519ksg^{2}}=\frac{125\times 4gh_{4}ks}{778519ksg^{2}}$$

Dividing by 6228.152g^{2}sk undoes the multiplication by 6228.152g^{2}sk.

$$J=\frac{125\times 4gh_{4}ks}{778519ksg^{2}}$$

Divide 4gh_{4}ks by 6228.152g^{2}sk.

$$J=\frac{500h_{4}}{778519g}$$

Solve for g

$$\left\{\begin{matrix}\\g\neq 0\text{, }&\text{unconditionally}\\g=\frac{500h_{4}}{778519J}\text{, }&h_{4}\neq 0\text{ and }J\neq 0\text{ and }s\neq 0\text{ and }k\neq 0\end{matrix}\right.$$