How would you solve for x given the equation:
(x/58.45) + ((0.86 - x)/74.55) = 0.01349
To solve for x in the equation:
(x/58.45) + ((0.86 - x)/74.55) = 0.01349
we can follow these steps:
Step 1: Multiply both sides of the equation by the least common multiple (LCM) of the denominators to clear out the fractions. In this case, the LCM of 58.45 and 74.55 is 4331.6475 (rounded to four decimal places).
4331.6475 * (x/58.45) + 4331.6475 * ((0.86 - x)/74.55) = 4331.6475 * 0.01349
Simplifying, we get:
74.265 * x + 58.45 * (0.86 - x) = 58.45 * 0.01349
Step 2: Distribute the terms on the left side of the equation:
74.265 * x + 50.327 - 58.45 * x = 0.7868005
Step 3: Combine like terms:
(74.265 - 58.45) * x + 50.327 = 0.7868005
15.815 * x + 50.327 = 0.7868005
Step 4: Move the constant term to the right side of the equation:
15.815 * x = 0.7868005 - 50.327
15.815 * x = -49.5401995
Step 5: Solve for x by dividing both sides of the equation by 15.815:
x = (-49.5401995) / 15.815
Simplifying, we find:
x ≈ -3.1328
Therefore, the solution for x is approximately -3.1328.