Solve for x.
5/8(x+1/2)=100
(1 point)
Responses
160 1/2
160 and 1 half
62
62
159 1/2
159 and 1 half
63
To solve for x, we will follow these steps:
1. Distribute the 5/8 to both terms inside the parentheses:
(5/8)x + (5/8)(1/2) = 100
This simplifies to:
(5/8)x + 5/16 = 100
2. Move the constant term (5/16) to the other side of the equation by subtracting it from both sides:
(5/8)x = 100 - 5/16
3. Simplify the right side of the equation:
(5/8)x = 160 - 5/16
Finding a common denominator for 8 and 16, we get:
(5/8)x = (2560/16) - (5/16)
This simplifies to:
(5/8)x = 2555/16
4. Multiply both sides of the equation by the reciprocal of 5/8, which is 8/5:
(8/5)(5/8)x = (8/5)(2555/16)
Simplifying both sides:
x = (2040/40)/(816/40)
This simplifies to:
x = 51/2
So, x = 51/2 or x = 25.5.