Let's solve the given problem step by step.
We start with the initial equation:
[tex]\[ \frac{x}{4} + \frac{5}{2} = \frac{-3}{3} \][/tex]
Step 1: Simplify the right-hand side.
[tex]\[ \frac{-3}{3} = -1 \][/tex]
So, the equation becomes:
[tex]\[ \frac{x}{4} + \frac{5}{2} = -1 \][/tex]
Step 2: Transpose \(\frac{5}{2}\) to the right-hand side. Remember, transposing means changing the side of a term while changing its sign.
[tex]\[ \frac{x}{4} = -1 - \frac{5}{2} \][/tex]
Step 3: Combine the terms on the right-hand side. To do this, we need a common denominator. The common denominator between 1 (or 2/2) and 2 is 2.
[tex]\[ -1 = \frac{-2}{2} \][/tex]
So, we combine:
[tex]\[ \frac{x}{4} = \frac{-2}{2} - \frac{5}{2} \][/tex]
[tex]\[ \frac{x}{4} = \frac{-2 - 5}{2} \][/tex]
[tex]\[ \frac{x}{4} = \frac{-7}{2} \][/tex]
Step 4: Observe the result of the transposition.
Given the options:
(A) [tex]\[ \frac{x}{4} = \frac{-3}{4} + \frac{5}{2} \][/tex]
(B) [tex]\[ \frac{x}{4} = \frac{-5}{2} + \frac{3}{4} \][/tex]
(C) [tex]\[ \frac{x}{4} = \frac{-3}{4} + (-\frac{5}{2}) \][/tex]
(D) none of these
None of the options match \(\frac{x}{4} = \frac{-7}{2}\). Hence, the correct choice is:
(D) none of these
