Question

You are solving the equation 0.02x - 0.004 = 0.028. Your first step is to multiply both sides by 1000 to clear the decimals. Your classmate starts by dividing both sides by 0.02. Is there any disadvantage to your classmate's method? Explain why one method might be preferred over the other when solving this equation.

Answer 1

Multiplying both sides by 1000 to clear the decimals is preferred over dividing both sides by 0.02 because it eliminates the decimals and simplifies the equation.

Step-by-step explanation:

In this case, the student wants to solve the equation 0.02x - 0.004 = 0.028. Your classmate's method of dividing both sides by 0.02 is not advantageous because it doesn't eliminate the decimals. Dividing by 0.02 would give you x - 0.2 = 1.4. This method would require additional steps to solve, whereas multiplying both sides by 1000 to clear the decimals right away would give you 20x - 4 = 28.

By multiplying both sides by 1000, we get 20x - 4 = 28. From here, we can proceed to solve the equation by adding 4 to both sides to isolate the variable, resulting in 20x = 32. Finally, dividing both sides by 20, we find that x = 1.6.