Step 1: Clear the fractions
To solve the equation 5x + 7/2 = 3/2x - 14, we need to first get rid of the fractions. To do this, we can multiply every term in the equation by the least common multiple (LCM) of the denominators, which in this case is 2.
Multiplying every term by 2, we get:
2(5x) + 2(7/2) = 2(3/2x) - 2(14)
10x + 7 = 3x - 28

Step 2: Combine like terms
Next, we need to combine like terms on each side of the equation. This involves adding or subtracting terms with the same variable.
10x - 3x = -28 - 7
7x = -35

Step 3: Solve for x
Now that we have 7x = -35, we can solve for x by dividing both sides by 7:
x = -35/7
x = -5

Step 4: Check the solution
To verify that x = -5 is the correct solution, we can substitute it back into the original equation:
5(-5) + 7/2 = 3/2(-5) - 14
-25 + 7/2 = -15/2 - 14
-25 + 3.5 = -7.5 - 14
-21.5 = -21.5
Since both sides of the equation are equal, x = -5 is the correct solution.

I am busy I will answer this later