Solve for x.

Question

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

Answer 1

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.