Find the Domain 5x+7/2=3/2x-14

Problem

(5*x+7)/2=3/(2*x−14)

Solution

1. Identify the expression as an equation involving rational terms.

2. Recall that the domain of an expression or equation consists of all real numbers except those that make any denominator equal to zero.

3. Set the denominators equal to zero to find the excluded values.

4. Observe that the first denominator is 2 which is a constant and never zero.

5. Solve for x in the second denominator: 2*x−14=0

6. Isolate the variable by adding 14 to both sides: 2*x=14

7. Divide by 2 to find the restricted value: x=7

8. Conclude that the domain includes all real numbers except x=7

Final Answer

Domain: *{x|x∈ℝ,x≠7}

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