Solve 0.00692=(0.0046+z(0.004))*0.004

$$0.00692 = ( 0.0046 + z ( 0.004 ) ) * 0.004$$

Solve for z

$$z=431.35$$

Steps for Solving Linear Equation

Divide both sides by 0.004.

$$\frac{0.00692}{0.004}=0.0046+z\times 0.004$$

Expand \frac{0.00692}{0.004} by multiplying both numerator and the denominator by 100000.

$$\frac{692}{400}=0.0046+z\times 0.004$$

Reduce the fraction \frac{692}{400} to lowest terms by extracting and canceling out 4.

$$\frac{173}{100}=0.0046+z\times 0.004$$

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

$$0.0046+z\times 0.004=\frac{173}{100}$$

Subtract 0.0046 from both sides.

$$z\times 0.004=\frac{173}{100}-0.0046$$

Convert decimal number 0.0046 to fraction \frac{46}{10000}. Reduce the fraction \frac{46}{10000} to lowest terms by extracting and canceling out 2.

$$z\times 0.004=\frac{173}{100}-\frac{23}{5000}$$

Least common multiple of 100 and 5000 is 5000. Convert \frac{173}{100} and \frac{23}{5000} to fractions with denominator 5000.

$$z\times 0.004=\frac{8650}{5000}-\frac{23}{5000}$$

Since \frac{8650}{5000} and \frac{23}{5000} have the same denominator, subtract them by subtracting their numerators.

$$z\times 0.004=\frac{8650-23}{5000}$$

Subtract 23 from 8650 to get 8627.

$$z\times 0.004=\frac{8627}{5000}$$

Divide both sides by 0.004.

$$z=\frac{\frac{8627}{5000}}{0.004}$$

Express \frac{\frac{8627}{5000}}{0.004} as a single fraction.

$$z=\frac{8627}{5000\times 0.004}$$

Multiply 5000 and 0.004 to get 20.

$$z=\frac{8627}{20}$$