To solve the equation 5/8 (x-1/2) = 10

Answer 1

To solve the equation 5/8 (x-1/2) = 10, we need to isolate x on one side of the equation.

First, let's distribute the 5/8 to both terms inside the parentheses:

(5/8) * (x - 1/2) = 10
(5/8) * x - (5/8) * (1/2) = 10
(5/8) * x - 5/16 = 10

Next, we can add 5/16 to both sides to move the constant term to the other side of the equation:

(5/8) * x - 5/16 + 5/16 = 10 + 5/16
(5/8) * x = 160/16 + 5/16
(5/8) * x = 165/16

Now, we can simplify the right side by converting it to a common denominator:

(5/8) * x = (165 + 5)/16
(5/8) * x = 170/16

Next, we can multiply both sides of the equation by the reciprocal of (5/8), which is (8/5):

[(5/8) * x] * (8/5) = (170/16) * (8/5)
x = (170 * 8) / (16 * 5)
x = 1360/80
x = 17/1

So the solution to the equation is x = 17.