Apologies for the mistake. Let's correct it.
To solve for x, we can start by simplifying the left side of the equation:
(5/8)(x + 1/2) = 100
Multiplying both terms within the parentheses by 5/8:
5/8 * x + 5/8 * 1/2 = 100
Simplifying:
5/8 * x + 5/16 = 100
Next, let's isolate the term with x by subtracting 5/16 from both sides:
5/8 * x = 100 - 5/16
To make the right side of the equation have a common denominator, we multiply 100 by 16/16:
5/8 * x = (1600/16) - (5/16)
Simplifying:
5/8 * x = 1595/16
To solve for x, we need to multiply both sides by the reciprocal of 5/8, which is 8/5:
x = (1595/16)(8/5)
Multiplying:
x = (1595 * 8) / (16 * 5)
x = 12760 / 80
Simplifying:
x = 159.5
Therefore, the solution for x is 159.5.