Final answer:
The solution to the equation (1/2)x + 3/2(x + 1) - 1/4 = 5 is 15/8, which corresponds to option (c). This is found by combining like terms, obtaining a common denominator, performing subtraction, and finally dividing by 2.
Step-by-step explanation:
To solve the equation (1/2)x + 3/2(x + 1) - 1/4 = 5, let's start by distributing the 3/2 across the x + 1. This gives us:
(1/2)x + (3/2)x + (3/2)*1 - 1/4 = 5
Now combine like terms:
(1/2 + 3/2)x + 3/2 - 1/4 = 5
Which simplifies to:
2x + 3/2 - 1/4 = 5
To combine the fractions, we need a common denominator. As we know, the lowest common denominator between 2 and 4 is 4, so we rewrite the fractions:
2x + 6/4 - 1/4 = 5
Combine the fractions:
2x + (6/4 - 1/4) = 5
2x + 5/4 = 5
Subtract 5/4 from both sides to get:
2x = 5 - 5/4
To subtract the fraction from 5, we rewrite 5 as 20/4:
2x = 20/4 - 5/4
2x = 15/4
Divide both sides by 2:
x = (15/4) / 2
x = 15/8
Therefore, the solution to the equation is 15/8 or option (c).